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Tim Leung

Personal Details

First Name:Tim
Middle Name:
Last Name:Leung
Suffix:
RePEc Short-ID:ple640
http://faculty.washington.edu/timleung/
Tim S.T. Leung Associate Professor Director, Computational Finance & Risk Management (CFRM) program Department of Applied Mathematics University of Washington Lewis Hall #217, Box 353925, Seattle, WA 98195-3925

Affiliation

University of Washington (University of Washington)

http://depts.washington.edu/amath/
Seattle, WA USA

Research output

as
Jump to: Working papers Articles Books

Working papers

  1. Tim Leung & Brian Ward, 2019. "Tracking VIX with VIX Futures: Portfolio Construction and Performance," Papers 1907.00293, arXiv.org.
  2. Tim Leung & Yang Zhou, 2019. "A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock Options," Papers 1906.03562, arXiv.org.
  3. Jize Zhang & Tim Leung & Aleksandr Aravkin, 2018. "A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization," Papers 1810.10563, arXiv.org.
  4. Jize Zhang & Tim Leung & Aleksandr Y. Aravkin, 2018. "Mean Reverting Portfolios via Penalized OU-Likelihood Estimation," Papers 1803.06460, arXiv.org.
  5. Bahman Angoshtari & Tim Leung, 2018. "Optimal Dynamic Basis Trading," Papers 1809.05961, arXiv.org, revised May 2019.
  6. Tim Leung & Raphael Yan, 2018. "A Stochastic Control Approach to Managed Futures Portfolios," Papers 1811.01916, arXiv.org.
  7. Tim Leung & Brian Ward, 2017. "Dynamic Index Tracking and Risk Exposure Control Using Derivatives," Papers 1705.10454, arXiv.org.
  8. Tim Leung & Jiao Li & Xin Li, 2017. "Optimal Timing to Trade Along a Randomized Brownian Bridge," Papers 1801.00372, arXiv.org, revised Aug 2018.
  9. Tim Leung & Yerkin Kitapbayev, 2017. "Optimal Mean-Reverting Spread Trading: Nonlinear Integral Equation Approach," Papers 1701.00875, arXiv.org, revised Jan 2017.
  10. Yerkin Kitapbayev & Tim Leung, 2017. "Mean Reversion Trading with Sequential Deadlines and Transaction Costs," Papers 1707.03498, arXiv.org, revised Jan 2018.
  11. Tim Leung & Hongzhong Zhang, 2017. "Optimal Trading with a Trailing Stop," Papers 1701.03960, arXiv.org, revised Mar 2019.
  12. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
  13. Tim Leung & Jamie Kang, 2016. "Asynchronous ADRs: Overnight vs Intraday Returns and Trading Strategies," Papers 1611.03110, arXiv.org.
  14. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Papers 1601.04210, arXiv.org.
  15. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2016. "Optimal Execution of Limit and Market Orders with Trade Director, Speed Limiter, and Fill Uncertainty," Papers 1604.04963, arXiv.org, revised Apr 2017.
  16. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
  17. Tim Leung & Hyungbin Park, 2016. "Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction Approach," Papers 1612.01013, arXiv.org.
  18. Kevin Guo & Tim Leung, 2016. "Understanding the Tracking Errors of Commodity Leveraged ETFs," Papers 1610.09404, arXiv.org.
  19. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.
  20. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.
  21. Eric Dahlgren & Tim Leung, 2015. "An Optimal Multiple Stopping Approach to Infrastructure Investment Decisions," Papers 1502.00861, arXiv.org.
  22. Tim Leung & Matthew Lorig, 2015. "Optimal Static Quadratic Hedging," Papers 1506.02074, arXiv.org, revised Nov 2015.
  23. Tim Leung & Yoshihiro Shirai, 2015. "Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties," Papers 1502.00358, arXiv.org.
  24. Jinbeom Kim & Tim Leung, 2015. "Pricing Derivatives with Counterparty Risk and Collateralization: A Fixed Point Approach," Papers 1501.06221, arXiv.org.
  25. Tim Leung & Brian Ward, 2015. "The Golden Target: Analyzing the Tracking Performance of Leveraged Gold ETFs," Papers 1501.02276, arXiv.org, revised Jan 2015.
  26. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
  27. Tim Leung & Haohua Wan, 2015. "ESO Valuation with Job Termination Risk and Jumps in Stock Price," Papers 1504.08073, arXiv.org.
  28. Tim Leung & Marco Santoli, 2014. "Accounting for Earnings Announcements in the Pricing of Equity Options," Papers 1412.8414, arXiv.org, revised Apr 2015.
  29. Tim Leung & Matthew Lorig & Andrea Pascucci, 2014. "Leveraged {ETF} implied volatilities from {ETF} dynamics," Papers 1404.6792, arXiv.org, revised Apr 2015.
  30. Tim Leung & Xin Li, 2014. "Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit," Papers 1411.5062, arXiv.org, revised May 2015.
  31. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
  32. Hongzhong Zhang & Tim Leung & Olympia Hadjiliadis, 2013. "Stochastic Modeling and Fair Valuation of Drawdown Insurance," Papers 1310.3860, arXiv.org.
  33. Tim Leung & Qingshuo Song & Jie Yang, 2011. "Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing," Papers 1109.5316, arXiv.org, revised Mar 2013.
  34. Masahiko Egami & Tim S. T. Leung & Kazutoshi Yamazaki, 2011. "Default Swap Games Driven by Spectrally Negative Levy Processes," Papers 1105.0238, arXiv.org, revised Sep 2012.
  35. Tim Leung & Peng Liu, 2011. "Risk Premia and Optimal Liquidation of Credit Derivatives," Papers 1110.0220, arXiv.org, revised Oct 2012.
  36. Tim Leung & Michael Ludkovski, 2010. "Optimal Timing to Purchase Options," Papers 1008.3650, arXiv.org, revised Apr 2011.
  37. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.
  38. S. Sheng & C.Y. Wong & L. Lessassy & K. Lai & T. Leung & Bao Yang, 2010. "Relational Adaptation in Buyer-Supplier Relationship Management: A Synthesis of Effects of Exchange Hazards, Relational Norms, and Legitimacy management: A synthesis of effects of exchange hazards, re," Post-Print hal-02108777, HAL.

Articles

  1. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
  2. Tim Leung & Raphael Yan, 2019. "A stochastic control approach to managed futures portfolios," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-22, March.
  3. Ryan Donnelly & Tim Leung, 2019. "Effort Expenditure For Cash Flow In A Mean-Field Equilibrium," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-23, June.
  4. Kevin Guo & Tim Leung & Brian Ward, 2019. "How to mine gold without digging," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-30, March.
  5. Tim Leung & Brian Ward, 2018. "Dynamic Index Tracking and Risk Exposure Control Using Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(2), pages 180-212, March.
  6. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
  7. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.
  8. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
  9. Jamie Kang & Tim Leung, 2017. "Asynchronous ADRs: overnight vs intraday returns and trading strategies," Studies in Economics and Finance, Emerald Group Publishing, vol. 34(4), pages 580-596, October.
  10. Tim Leung & Matthew Lorig & Andrea Pascucci, 2017. "Leveraged Etf Implied Volatilities From Etf Dynamics," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1035-1068, October.
  11. Tim Leung & Hyungbin Park, 2017. "LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-33, September.
  12. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2017. "Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
  13. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
  14. Guo, Kevin & Leung, Tim, 2017. "Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options," Journal of Commodity Markets, Elsevier, vol. 6(C), pages 32-49.
  15. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
  16. Tim Leung & Matthew Lorig, 2016. "Optimal static quadratic hedging," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1341-1355, September.
  17. Kim, Jinbeom & Leung, Tim, 2016. "Pricing derivatives with counterparty risk and collateralization: A fixed point approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 525-539.
  18. Owen Williams, 2016. "Foreign currency exposure within country exchange traded funds," Studies in Economics and Finance, Emerald Group Publishing, vol. 33(2), pages 222-243, June.
  19. Jinbeom Kim & Tim Leung, 2016. "Impact of risk aversion and belief heterogeneity on trading of defaultable claims," Annals of Operations Research, Springer, vol. 243(1), pages 117-146, August.
  20. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing, vol. 32(3), pages 278-297, August.
  21. Tim Leung & Ronnie Sircar, 2015. "Implied Volatility of Leveraged ETF Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 162-188, April.
  22. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
  23. Dahlgren, Eric & Leung, Tim, 2015. "An optimal multiple stopping approach to infrastructure investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 251-267.
  24. Tim Leung & Yoshihiro Shirai, 2015. "Optimal derivative liquidation timing under path-dependent risk penalties," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-32.
  25. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
  26. Tim Leung & Marco Santoli, 2014. "Accounting for earnings announcements in the pricing of equity options," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-46.
  27. Tim Leung & Kazutoshi Yamazaki, 2013. "American step-up and step-down default swaps under Lévy models," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 137-157, January.
  28. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.
  29. Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
  30. Tim Leung & Qingshuo Song & Jie Yang, 2013. "Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing," Finance and Stochastics, Springer, vol. 17(4), pages 839-870, October.
  31. Tim Leung & Peng Liu, 2012. "Risk Premia And Optimal Liquidation Of Credit Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-34.
  32. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128.

Books

  1. Tim Leung & Xin Li, 2016. "Optimal Mean Reversion Trading:Mathematical Analysis and Practical Applications," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9839, September.

Citations

Many of the citations below have been collected in an experimental project, CitEc, where a more detailed citation analysis can be found. These are citations from works listed in RePEc that could be analyzed mechanically. So far, only a minority of all works could be analyzed. See under "Corrections" how you can help improve the citation analysis.

Working papers

  1. Bahman Angoshtari & Tim Leung, 2018. "Optimal Dynamic Basis Trading," Papers 1809.05961, arXiv.org, revised May 2019.

    Cited by:

    1. Tim Leung & Raphael Yan, 2018. "A Stochastic Control Approach to Managed Futures Portfolios," Papers 1811.01916, arXiv.org.

  2. Tim Leung & Brian Ward, 2017. "Dynamic Index Tracking and Risk Exposure Control Using Derivatives," Papers 1705.10454, arXiv.org.

    Cited by:

    1. Tim Leung & Raphael Yan, 2018. "A Stochastic Control Approach to Managed Futures Portfolios," Papers 1811.01916, arXiv.org.

  3. Tim Leung & Jiao Li & Xin Li, 2017. "Optimal Timing to Trade Along a Randomized Brownian Bridge," Papers 1801.00372, arXiv.org, revised Aug 2018.

    Cited by:

    1. Bahman Angoshtari & Tim Leung, 2018. "Optimal Dynamic Basis Trading," Papers 1809.05961, arXiv.org, revised May 2019.
    2. Leunglung Chan, 2018. "Editorial for Special Issue “Finance, Financial Risk Management and their Applications”," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(4), pages 1-3, October.
    3. Tiziano De Angelis & Alessandro Milazzo, 2019. "Optimal stopping for the exponential of a Brownian bridge," Papers 1904.00075, arXiv.org.

  4. Tim Leung & Yerkin Kitapbayev, 2017. "Optimal Mean-Reverting Spread Trading: Nonlinear Integral Equation Approach," Papers 1701.00875, arXiv.org, revised Jan 2017.

    Cited by:

    1. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
    2. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.

  5. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Papers 1601.04210, arXiv.org.

    Cited by:

    1. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
    2. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    3. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
    4. Tim Leung & Raphael Yan, 2018. "A Stochastic Control Approach to Managed Futures Portfolios," Papers 1811.01916, arXiv.org.
    5. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    6. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    7. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.
    8. Zhou, Liyun & Zhang, Rixin & Huang, Jialiang, 2019. "Investor trading behavior on agricultural future prices," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 365-379.

  6. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2016. "Optimal Execution of Limit and Market Orders with Trade Director, Speed Limiter, and Fill Uncertainty," Papers 1604.04963, arXiv.org, revised Apr 2017.

    Cited by:

    1. Xue Cheng & Marina Di Giacinto & Tai-Ho Wang, 2019. "Optimal execution with dynamic risk adjustment," Papers 1901.00617, arXiv.org, revised Jul 2019.
    2. Bahman Angoshtari & Tim Leung, 2018. "Optimal Dynamic Basis Trading," Papers 1809.05961, arXiv.org, revised May 2019.

  7. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.

    Cited by:

    1. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.

  8. Tim Leung & Hyungbin Park, 2016. "Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction Approach," Papers 1612.01013, arXiv.org.

    Cited by:

    1. Nian Yao, 2018. "Optimal leverage ratio estimate of various models for leveraged ETFs to exceed a target: Probability estimates of large deviations," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-37, June.

  9. Kevin Guo & Tim Leung, 2016. "Understanding the Tracking Errors of Commodity Leveraged ETFs," Papers 1610.09404, arXiv.org.

    Cited by:

    1. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
    2. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing, vol. 32(3), pages 278-297, August.
    3. Paolo Guasoni & Eberhard Mayerhofer, 2015. "The Limits of Leverage," Papers 1506.02802, arXiv.org, revised Oct 2017.
    4. Jamie Kang & Tim Leung, 2017. "Asynchronous ADRs: overnight vs intraday returns and trading strategies," Studies in Economics and Finance, Emerald Group Publishing, vol. 34(4), pages 580-596, October.
    5. Tim Leung & Matthew Lorig & Andrea Pascucci, 2014. "Leveraged {ETF} implied volatilities from {ETF} dynamics," Papers 1404.6792, arXiv.org, revised Apr 2015.

  10. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.

    Cited by:

    1. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.
    2. Pérez, José-Luis & Yamazaki, Kazutoshi, 2017. "On the optimality of periodic barrier strategies for a spectrally positive Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 1-13.
    3. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Double continuation regions for American and Swing options with negative discount rate in L\'evy models," Papers 1801.00266, arXiv.org, revised Jan 2019.
    4. Neofytos Rodosthenous & Hongzhong Zhang, 2017. "Beating the Omega Clock: An Optimal Stopping Problem with Random Time-horizon under Spectrally Negative L\'evy Models," Papers 1706.03724, arXiv.org.

  11. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.

    Cited by:

    1. Jos'e-Luis P'erez & Kazutoshi Yamazaki & Alain Bensoussan, 2018. "Optimal periodic replenishment policies for spectrally positive L\'evy demand processes," Papers 1806.09216, arXiv.org.
    2. Kei Noba & Jos'e-Luis P'erez & Kazutoshi Yamazaki & Kouji Yano, 2017. "On optimal periodic dividend strategies for L\'evy risk processes," Papers 1708.01678, arXiv.org, revised Feb 2018.
    3. Mingsi Long & Hongzhong Zhang, 2017. "On the optimality of threshold type strategies in single and recursive optimal stopping under L\'evy models," Papers 1707.07797, arXiv.org, revised Aug 2018.
    4. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.
    5. Pérez, José-Luis & Yamazaki, Kazutoshi, 2017. "On the optimality of periodic barrier strategies for a spectrally positive Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 1-13.
    6. Czarna, Irmina & Pérez, José-Luis & Yamazaki, Kazutoshi, 2018. "Optimality of multi-refraction control strategies in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 148-160.
    7. Jos'e-Luis P'erez & Kazutoshi Yamazaki, 2016. "Hybrid continuous and periodic barrier strategies in the dual model: optimality and fluctuation identities," Papers 1612.02444, arXiv.org, revised Jan 2018.
    8. Noba, Kei & Pérez, José-Luis & Yamazaki, Kazutoshi & Yano, Kouji, 2018. "On optimal periodic dividend strategies for Lévy risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 29-44.

  12. Eric Dahlgren & Tim Leung, 2015. "An Optimal Multiple Stopping Approach to Infrastructure Investment Decisions," Papers 1502.00861, arXiv.org.

    Cited by:

    1. Álvaro Cartea & Sebastian Jaimungal, 2017. "Irreversible Investments And Ambiguity Aversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(07), pages 1-26, November.
    2. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.
    3. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.
    4. Carol Alexander & Xi Chen, 2018. "Model Risk in Real Option Valuation," Papers 1809.00817, arXiv.org, revised Sep 2018.
    5. Klaus Eisenack & Marius Paschen, 2017. "Designing long-lived investments under uncertain and ongoing change," Working Papers V-398-17, University of Oldenburg, Department of Economics, revised Feb 2017.
    6. Ludkovski, Michael & Sircar, Ronnie, 2016. "Technology ladders and R&D in dynamic Cournot markets," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 127-151.

  13. Tim Leung & Matthew Lorig, 2015. "Optimal Static Quadratic Hedging," Papers 1506.02074, arXiv.org, revised Nov 2015.

    Cited by:

    1. Peter Carr & Roger Lee & Matthew Lorig, 2015. "Robust replication of barrier-style claims on price and volatility," Papers 1508.00632, arXiv.org, revised May 2017.

  14. Tim Leung & Yoshihiro Shirai, 2015. "Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties," Papers 1502.00358, arXiv.org.

    Cited by:

    1. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2017. "Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    2. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Papers 1601.04210, arXiv.org.
    3. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    4. Tim Leung & Xin Li, 2014. "Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit," Papers 1411.5062, arXiv.org, revised May 2015.
    5. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    6. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
    7. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.
    8. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.

  15. Jinbeom Kim & Tim Leung, 2015. "Pricing Derivatives with Counterparty Risk and Collateralization: A Fixed Point Approach," Papers 1501.06221, arXiv.org.

    Cited by:

    1. Harb, Etienne & Louhichi, Wael, 2017. "Pricing CDS spreads with Credit Valuation Adjustment using a mixture copula," Research in International Business and Finance, Elsevier, vol. 39(PB), pages 963-975.
    2. Brigo, Damiano & Francischello, Marco & Pallavicini, Andrea, 2019. "Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement," European Journal of Operational Research, Elsevier, vol. 274(2), pages 788-805.
    3. Ballotta, Laura & Fusai, Gianluca & Marazzina, Daniele, 2019. "Integrated structural approach to Credit Value Adjustment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1143-1157.
    4. Cheikh Mbaye & Fr'ed'eric Vrins, 2019. "Affine term structure models : a time-changed approach with perfect fit to market curves," Papers 1903.04211, arXiv.org, revised Mar 2019.
    5. Damiano Brigo & Frédéric Vrins, 2018. "Disentangling wrong-way risk: Pricing credit valuation adjustment via change of measures," CORE Discussion Papers RP 2949, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

  16. Tim Leung & Brian Ward, 2015. "The Golden Target: Analyzing the Tracking Performance of Leveraged Gold ETFs," Papers 1501.02276, arXiv.org, revised Jan 2015.

    Cited by:

    1. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
    2. Tim Leung & Hyungbin Park, 2016. "Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction Approach," Papers 1612.01013, arXiv.org.
    3. Gregor Dorfleitner & Anna Gerl & Johannes Gerer, 2018. "The pricing efficiency of exchange-traded commodities," Review of Managerial Science, Springer, vol. 12(1), pages 255-284, January.

  17. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.

    Cited by:

    1. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
    2. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    3. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    4. Eric Dahlgren & Tim Leung, 2015. "An Optimal Multiple Stopping Approach to Infrastructure Investment Decisions," Papers 1502.00861, arXiv.org.
    5. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    6. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Papers 1601.04210, arXiv.org.
    7. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    8. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    9. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    10. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
    11. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    12. Zuo Quan Xu & Fahuai Yi, 2019. "Optimal redeeming strategy of stock loans under drift uncertainty," Papers 1901.06680, arXiv.org.
    13. Tim Leung & Hongzhong Zhang, 2017. "Optimal Trading with a Trailing Stop," Papers 1701.03960, arXiv.org, revised Mar 2019.
    14. Peng Huang & Tianxiang Wang, 2016. "On the Profitability of Optimal Mean Reversion Trading Strategies," Papers 1602.05858, arXiv.org.

  18. Tim Leung & Marco Santoli, 2014. "Accounting for Earnings Announcements in the Pricing of Equity Options," Papers 1412.8414, arXiv.org, revised Apr 2015.

    Cited by:

    1. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.

  19. Tim Leung & Matthew Lorig & Andrea Pascucci, 2014. "Leveraged {ETF} implied volatilities from {ETF} dynamics," Papers 1404.6792, arXiv.org, revised Apr 2015.

    Cited by:

    1. Tim Leung & Hyungbin Park, 2016. "Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction Approach," Papers 1612.01013, arXiv.org.
    2. Vasiliki A. Basdekidou, 2017. "The Leveraged ETF Inefficiency in Trending & Range-Bound Markets: An Application Case Study for a 3x Leveraged Gold Miners ETF," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 9(7), pages 1-13, July.
    3. Tim Leung & Brian Ward, 2018. "Dynamic Index Tracking and Risk Exposure Control Using Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(2), pages 180-212, March.
    4. Tim Leung & Matthew Lorig, 2015. "Optimal Static Quadratic Hedging," Papers 1506.02074, arXiv.org, revised Nov 2015.

  20. Tim Leung & Xin Li, 2014. "Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit," Papers 1411.5062, arXiv.org, revised May 2015.

    Cited by:

    1. Endres, Sylvia & Stübinger, Johannes, 2017. "Optimal trading strategies for Lévy-driven Ornstein-Uhlenbeck processes," FAU Discussion Papers in Economics 17/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    2. Alvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2018. "Trading Cointegrated Assets with Price Impact," Papers 1807.01428, arXiv.org.
    3. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
    4. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing, vol. 32(3), pages 278-297, August.
    5. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    6. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    7. Roberto Baviera & Tommaso Santagostino Baldi, 2017. "Stop-loss and Leverage in optimal Statistical Arbitrage with an application to Energy market," Papers 1706.07021, arXiv.org.
    8. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.
    9. Aïd, René & Li, Liangchen & Ludkovski, Michael, 2017. "Capacity expansion games with application to competition in power generation investments," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 1-31.
    10. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    11. Liangchen Li & Michael Ludkovski, 2018. "Stochastic Switching Games," Papers 1807.03893, arXiv.org.
    12. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Papers 1601.04210, arXiv.org.
    13. Jorge Guijarro-Ordonez, 2019. "Stochastic control in high-dimensional statistical arbitrage under an Ornstein-Uhlenbeck process," Papers 1901.09309, arXiv.org.
    14. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    15. Dimitrios Vezeris & Themistoklis Kyrgos & Christos Schinas, 2018. "Take Profit and Stop Loss Trading Strategies Comparison in Combination with an MACD Trading System," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(3), pages 1-23, September.
    16. Minh Man Ngo & Huyen Pham, 2014. "Optimal switching for pairs trading rule: a viscosity solutions approach," Papers 1412.7649, arXiv.org.
    17. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    18. Jamie Kang & Tim Leung, 2017. "Asynchronous ADRs: overnight vs intraday returns and trading strategies," Studies in Economics and Finance, Emerald Group Publishing, vol. 34(4), pages 580-596, October.
    19. Johannes Stübinger & Lucas Schneider, 2019. "Statistical Arbitrage with Mean-Reverting Overnight Price Gaps on High-Frequency Data of the S&P 500," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 12(2), pages 1-19, April.
    20. de Angelis, Tiziano & Ferrari, Giorgio & Moriarty, John, 2016. "Nash equilibria of threshold type for two-player nonzero-sum games of stopping," Center for Mathematical Economics Working Papers 563, Center for Mathematical Economics, Bielefeld University.
    21. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    22. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
    23. Baurdoux, Erik J. & Chen, Nan & Surya, Budhi & Yamazak, Kazutoshi, 2015. "Optimal double stopping of a Brownian bridge," LSE Research Online Documents on Economics 61618, London School of Economics and Political Science, LSE Library.
    24. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    25. Álvaro Cartea & Sebastian Jaimungal & Jason Ricci, 2018. "Trading Strategies Within The Edges Of No-Arbitrage," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-37, May.
    26. Suhan Altay & Katia Colaneri & Zehra Eksi, 2017. "Pairs Trading under Drift Uncertainty and Risk Penalization," Papers 1704.06697, arXiv.org, revised Sep 2018.
    27. Thomas Nanfeng Li & Agnès Tourin, 2016. "Optimal pairs trading with time-varying volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-29, September.
    28. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    29. Tim Leung & Hongzhong Zhang, 2017. "Optimal Trading with a Trailing Stop," Papers 1701.03960, arXiv.org, revised Mar 2019.
    30. Sühan Altay & Katia Colaneri & Zehra Eksi, 2018. "Pairs Trading Under Drift Uncertainty And Risk Penalization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-24, November.
    31. Álvaro Cartea & Sebastian Jaimungal, 2016. "Algorithmic Trading Of Co-Integrated Assets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-18, September.
    32. Peng Huang & Tianxiang Wang, 2016. "On the Profitability of Optimal Mean Reversion Trading Strategies," Papers 1602.05858, arXiv.org.
    33. Erik J. Baurdoux & Nan Chen & Budhi A. Surya & Kazutoshi Yamazaki, 2014. "Optimal double stopping of a Brownian bridge," Papers 1409.2226, arXiv.org, revised Dec 2014.

  21. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.

    Cited by:

    1. Kevin Guo & Tim Leung, 2016. "Understanding the Non-Convergence of Agricultural Futures via Stochastic Storage Costs and Timing Options," Papers 1610.09403, arXiv.org, revised Apr 2017.
    2. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    3. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    4. Yerkin Kitapbayev & Tim Leung, 2018. "Mean Reversion Trading With Sequential Deadlines And Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-22, February.
    5. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Papers 1601.04210, arXiv.org.
    6. Tim Leung & Zheng Wang, 2019. "Optimal risk-averse timing of an asset sale: trending versus mean-reverting price dynamics," Annals of Finance, Springer, vol. 15(1), pages 1-28, March.
    7. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    8. Tim Leung & Zheng Wang, 2016. "Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics," Papers 1610.08143, arXiv.org.
    9. Tim Leung & Hongzhong Zhang, 2017. "Optimal Trading with a Trailing Stop," Papers 1701.03960, arXiv.org, revised Mar 2019.

  22. Hongzhong Zhang & Tim Leung & Olympia Hadjiliadis, 2013. "Stochastic Modeling and Fair Valuation of Drawdown Insurance," Papers 1310.3860, arXiv.org.

    Cited by:

    1. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    2. Ola Mahmoud, 2015. "The Temporal Dimension of Risk," Papers 1501.01573, arXiv.org, revised Jun 2016.
    3. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Fair valuation of L\'evy-type drawdown-drawup contracts with general insured and penalty functions," Papers 1712.04418, arXiv.org, revised Feb 2018.
    4. Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Pricing insurance drawdown-type contracts with underlying L\'evy assets," Papers 1701.01891, arXiv.org, revised Oct 2017.
    5. Baurdoux, E.J. & Palmowski, Z. & Pistorius, M.R., 2017. "On future drawdowns of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2679-2698.
    6. David Landriault & Bin Li & Hongzhong Zhang, 2014. "On the Frequency of Drawdowns for Brownian Motion Processes," Papers 1403.1183, arXiv.org.
    7. Zbigniew Palmowski & Joanna Tumilewicz, 2018. "Drawdown insurance contracts for the Lévy-type model with the phase-type jump distribution and general reward function," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 51, pages 255-270.
    8. Baurdoux, Erik J. & Palmowski, Z & Pistorius, Martijn R, 2017. "On future drawdowns of Lévy processes," LSE Research Online Documents on Economics 84342, London School of Economics and Political Science, LSE Library.
    9. Landriault, David & Li, Bin & Li, Shu, 2018. "Expected utility of the drawdown-based regime-switching risk model with state-dependent termination," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 137-147.
    10. Landriault, David & Li, Bin & Li, Shu, 2015. "Analysis of a drawdown-based regime-switching Lévy insurance model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 98-107.
    11. Palmowski, Zbigniew & Tumilewicz, Joanna, 2018. "Pricing insurance drawdown-type contracts with underlying Lévy assets," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 1-14.
    12. David Landriault & Bin Li & Hongzhong Zhang, 2017. "A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes," Papers 1702.07786, arXiv.org.
    13. Zbigniew Palmowski & Budhi Surya, 2019. "Optimal valuation of American callable credit default swaps under drawdown," Papers 1904.10063, arXiv.org.
    14. Landriault, David & Li, Bin & Wong, Jeff T.Y. & Xu, Di, 2018. "Poissonian potential measures for Lévy risk models," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 152-166.

  23. Tim Leung & Qingshuo Song & Jie Yang, 2011. "Outperformance Portfolio Optimization via the Equivalence of Pure and Randomized Hypothesis Testing," Papers 1109.5316, arXiv.org, revised Mar 2013.

    Cited by:

    1. Jan Obloj & Johannes Wiesel, 2018. "A unified Framework for Robust Modelling of Financial Markets in discrete time," Papers 1808.06430, arXiv.org.
    2. Erhan Bayraktar & Gu Wang, 2014. "Quantile Hedging in a Semi-Static Market with Model Uncertainty," Papers 1408.4848, arXiv.org, revised Sep 2017.
    3. Yao Tung Huang & Qingshuo Song & Harry Zheng, 2015. "Weak Convergence of Path-Dependent SDEs in Basket CDS Pricing with Contagion Risk," Papers 1506.00082, arXiv.org, revised May 2016.
    4. Ji, Shaolin & Shi, Xiaomin, 2018. "Reaching goals under ambiguity: Continuous-time optimal portfolio selection," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 63-69.

  24. Masahiko Egami & Tim S. T. Leung & Kazutoshi Yamazaki, 2011. "Default Swap Games Driven by Spectrally Negative Levy Processes," Papers 1105.0238, arXiv.org, revised Sep 2012.

    Cited by:

    1. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2727-2751.
    2. Mingsi Long & Hongzhong Zhang, 2017. "On the optimality of threshold type strategies in single and recursive optimal stopping under L\'evy models," Papers 1707.07797, arXiv.org, revised Aug 2018.
    3. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," LSE Research Online Documents on Economics 61617, London School of Economics and Political Science, LSE Library.
    4. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.
    5. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    6. Kazutoshi Yamazaki, 2016. "Optimality of two-parameter strategies in stochastic control," Papers 1605.04995, arXiv.org.
    7. Hernández-Hernández, Daniel & Yamazaki, Kazutoshi, 2015. "Games of singular control and stopping driven by spectrally one-sided Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 1-38.

  25. Tim Leung & Peng Liu, 2011. "Risk Premia and Optimal Liquidation of Credit Derivatives," Papers 1110.0220, arXiv.org, revised Oct 2012.

    Cited by:

    1. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2017. "Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    2. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Papers 1601.04210, arXiv.org.
    3. Tim Leung & Yoshihiro Shirai, 2015. "Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties," Papers 1502.00358, arXiv.org.
    4. Tim Leung & Xin Li, 2014. "Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit," Papers 1411.5062, arXiv.org, revised May 2015.
    5. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    6. Kim, Jinbeom & Leung, Tim, 2016. "Pricing derivatives with counterparty risk and collateralization: A fixed point approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 525-539.
    7. Tim Leung & Xin Li & Zheng Wang, 2014. "Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs," Papers 1411.6080, arXiv.org.
    8. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.
    9. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    10. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.

  26. Tim Leung & Michael Ludkovski, 2010. "Optimal Timing to Purchase Options," Papers 1008.3650, arXiv.org, revised Apr 2011.

    Cited by:

    1. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, September.
    2. Tim Leung & Yoshihiro Shirai, 2015. "Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties," Papers 1502.00358, arXiv.org.
    3. Tim Leung & Peng Liu, 2012. "Risk Premia And Optimal Liquidation Of Credit Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-34.
    4. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    5. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.
    6. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.
    7. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    8. Tim Leung & Xin Li & Zheng Wang, 2015. "Optimal Multiple Trading Times Under the Exponential OU Model with Transaction Costs," Papers 1504.04682, arXiv.org.
    9. Tim Leung & Hongzhong Zhang, 2017. "Optimal Trading with a Trailing Stop," Papers 1701.03960, arXiv.org, revised Mar 2019.

  27. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.

    Cited by:

    1. Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
    2. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    3. Mitya Boyarchenko & Sergei Levendorskiĭ, 2015. "Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided Lévy models: the parabolic Laplace inversion method," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 421-441, March.
    4. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.
    5. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    6. Kazutoshi Yamazaki, 2016. "Optimality of two-parameter strategies in stochastic control," Papers 1605.04995, arXiv.org.
    7. Hernández-Hernández, Daniel & Yamazaki, Kazutoshi, 2015. "Games of singular control and stopping driven by spectrally one-sided Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 1-38.

Articles

  1. Tim Leung & Brian Ward, 2018. "Dynamic Index Tracking and Risk Exposure Control Using Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(2), pages 180-212, March.
    See citations under working paper version above.
  2. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," International Journal of Financial Studies, MDPI, Open Access Journal, vol. 6(3), pages 1-23, August.
    See citations under working paper version above.
  3. Tim Leung & Raphael Yan, 2018. "Optimal dynamic pairs trading of futures under a two-factor mean-reverting model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-23, September.

    Cited by:

    1. Tim Leung & Raphael Yan, 2018. "A Stochastic Control Approach to Managed Futures Portfolios," Papers 1811.01916, arXiv.org.

  4. Tim Leung & Matthew Lorig & Andrea Pascucci, 2017. "Leveraged Etf Implied Volatilities From Etf Dynamics," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1035-1068, October.

    Cited by:

    1. Olesya Grishchenko & Xiao Han & Victor Nistor, 2018. "A volatility-of-volatility expansion of the option prices in the SABR stochastic volatility model," Papers 1812.09904, arXiv.org.

  5. Tim Leung & Hyungbin Park, 2017. "LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-33, September. See citations under working paper version above.
  6. Brian Bulthuis & Julio Concha & Tim Leung & Brian Ward, 2017. "Optimal execution of limit and market orders with trade director, speed limiter, and fill uncertainty," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    See citations under working paper version above.
  7. Yerkin Kitapbayev & Tim Leung, 2017. "Optimal mean-reverting spread trading: nonlinear integral equation approach," Annals of Finance, Springer, vol. 13(2), pages 181-203, May.
    See citations under working paper version above.
  8. Guo, Kevin & Leung, Tim, 2017. "Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options," Journal of Commodity Markets, Elsevier, vol. 6(C), pages 32-49.
    See citations under working paper version above.
  9. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
    See citations under working paper version above.
  10. Tim Leung & Matthew Lorig, 2016. "Optimal static quadratic hedging," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1341-1355, September.
    See citations under working paper version above.
  11. Kim, Jinbeom & Leung, Tim, 2016. "Pricing derivatives with counterparty risk and collateralization: A fixed point approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 525-539. See citations under working paper version above.
  12. Jinbeom Kim & Tim Leung, 2016. "Impact of risk aversion and belief heterogeneity on trading of defaultable claims," Annals of Operations Research, Springer, vol. 243(1), pages 117-146, August.

    Cited by:

    1. Qing-Qing Yang & Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "On Optimal Pricing Model for Multiple Dealers in a Competitive Market," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 397-431, January.

  13. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing, vol. 32(3), pages 278-297, August.
    See citations under working paper version above.
  14. Tim Leung & Ronnie Sircar, 2015. "Implied Volatility of Leveraged ETF Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 162-188, April.

    Cited by:

    1. Hyungbin Park, 2018. "Sensitivity analysis of long-term cash flows," Finance and Stochastics, Springer, vol. 22(4), pages 773-825, October.
    2. Tim Leung & Brian Ward, 2015. "The golden target: analyzing the tracking performance of leveraged gold ETFs," Studies in Economics and Finance, Emerald Group Publishing, vol. 32(3), pages 278-297, August.
    3. Tim Leung & Hyungbin Park, 2016. "Long-Term Growth Rate of Expected Utility for Leveraged ETFs: Martingale Extraction Approach," Papers 1612.01013, arXiv.org.
    4. Tim Leung & Brian Ward, 2018. "Dynamic Index Tracking and Risk Exposure Control Using Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(2), pages 180-212, March.
    5. Tim Leung & Matthew Lorig & Andrea Pascucci, 2014. "Leveraged {ETF} implied volatilities from {ETF} dynamics," Papers 1404.6792, arXiv.org, revised Apr 2015.
    6. Tim Leung & Matthew Lorig, 2015. "Optimal Static Quadratic Hedging," Papers 1506.02074, arXiv.org, revised Nov 2015.

  15. Tim Leung & Xin Li, 2015. "Optimal Mean Reversion Trading With Transaction Costs And Stop-Loss Exit," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 1-31.
    See citations under working paper version above.
  16. Dahlgren, Eric & Leung, Tim, 2015. "An optimal multiple stopping approach to infrastructure investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 251-267.
    See citations under working paper version above.
  17. Tim Leung & Yoshihiro Shirai, 2015. "Optimal derivative liquidation timing under path-dependent risk penalties," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-32.
    See citations under working paper version above.
  18. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    See citations under working paper version above.
  19. Tim Leung & Marco Santoli, 2014. "Accounting for earnings announcements in the pricing of equity options," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-46.
    See citations under working paper version above.
  20. Tim Leung & Kazutoshi Yamazaki, 2013. "American step-up and step-down default swaps under Lévy models," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 137-157, January.
    See citations under working paper version above.
  21. Zhang, Hongzhong & Leung, Tim & Hadjiliadis, Olympia, 2013. "Stochastic modeling and fair valuation of drawdown insurance," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 840-850.
    See citations under working paper version above.
  22. Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
    See citations under working paper version above.
  23. Tim Leung & Qingshuo Song & Jie Yang, 2013. "Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing," Finance and Stochastics, Springer, vol. 17(4), pages 839-870, October.
    See citations under working paper version above.
  24. Tim Leung & Peng Liu, 2012. "Risk Premia And Optimal Liquidation Of Credit Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-34.
    See citations under working paper version above.
  25. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128.

    Cited by:

    1. Tiziano De Angelis & Yerkin Kitapbayev, 2014. "On the optimal exercise boundaries of swing put options," Papers 1407.6860, arXiv.org, revised Jan 2017.
    2. Ángel León Valle & Antonio Vaello & Julio Carmona, 2009. "Pricing executive stock options under employment shocks," Working Papers. Serie AD 2009-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Eric Dahlgren & Tim Leung, 2015. "An Optimal Multiple Stopping Approach to Infrastructure Investment Decisions," Papers 1502.00861, arXiv.org.
    4. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Oct 2018.
    5. Tim Leung & Kazutoshi Yamazaki, 2013. "American step-up and step-down default swaps under Lévy models," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 137-157, January.
    6. Martin Widdicks & Jinsha Zhao, 2014. "A Model of Equity Based Compensation with Tax," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 41(7-8), pages 1002-1041, September.
    7. Dandan Song & Zhaojun Yang, 2014. "Utility-Based Pricing, Timing and Hedging of an American Call Option Under an Incomplete Market with Partial Information," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 1-26, June.
    8. Tang, Chun-Hua, 2012. "Revisiting the incentive effects of executive stock options," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 564-574.
    9. Vicky Henderson & David Hobson, 2013. "Risk Aversion, Indivisible Timing Options, and Gambling," Operations Research, INFORMS, vol. 61(1), pages 126-137, February.
    10. Julio Carmona & Angel León & Antoni Vaello-Sebastià, 2010. "Pricing executive stock options under employment shocks," Post-Print hal-00753042, HAL.
    11. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Models," Papers 1505.07313, arXiv.org.
    12. Kim, Jinbeom & Leung, Tim, 2016. "Pricing derivatives with counterparty risk and collateralization: A fixed point approach," European Journal of Operational Research, Elsevier, vol. 249(2), pages 525-539.
    13. Abudy, Menachem & Benninga, Simon, 2013. "Non-marketability and the value of employee stock options," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5500-5510.
    14. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting," Papers 1505.07705, arXiv.org.
    15. Susana Álvarez-Díez & J. Baixauli-Soler & María Belda-Ruiz, 2014. "Are we using the wrong letters? An analysis of executive stock option Greeks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(2), pages 237-262, June.
    16. Carpenter, Jennifer N. & Stanton, Richard & Wallace, Nancy, 2010. "Optimal exercise of executive stock options and implications for firm cost," Journal of Financial Economics, Elsevier, vol. 98(2), pages 315-337, November.
    17. Colwell, David B. & Feldman, David & Hu, Wei, 2015. "Non-transferable non-hedgeable executive stock option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 161-191.
    18. Erhan Bayraktar & Virginia R. Young, 2007. "Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio," Papers math/0701650, arXiv.org, revised Jul 2007.
    19. Kamil Kladivko & Mihail Zervos, 2017. "Valuation of Employee Stock Options (ESOs) by means of Mean-Variance Hedging," Papers 1710.00897, arXiv.org.
    20. Gao, Jin & Ulm, Eric R., 2012. "Optimal consumption and allocation in variable annuities with Guaranteed Minimum Death Benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 586-598.
    21. Tim Leung & Haohua Wan, 2015. "ESO Valuation with Job Termination Risk and Jumps in Stock Price," Papers 1504.08073, arXiv.org.
    22. Xiaoshan Chen & Qingshuo Song & Fahuai Yi & George Yin, 2011. "Indifference Pricing of American Option Underlying Illiquid Stock under Exponential Forward Performance," Papers 1201.0075, arXiv.org.
    23. Alghalith, Moawia, 2012. "Forward dynamic utility functions: A new model and new results," European Journal of Operational Research, Elsevier, vol. 223(3), pages 842-845.

Books

  1. Tim Leung & Xin Li, 2016. "Optimal Mean Reversion Trading:Mathematical Analysis and Practical Applications," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9839, September.

    Cited by:

    1. Bahman Angoshtari & Tim Leung, 2018. "Optimal Dynamic Basis Trading," Papers 1809.05961, arXiv.org, revised May 2019.

More information

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Co-authorship network on CollEc

NEP Fields

NEP is an announcement service for new working papers, with a weekly report in each of many fields. This author has had 19 papers announced in NEP. These are the fields, ordered by number of announcements, along with their dates. If the author is listed in the directory of specialists for this field, a link is also provided.
  1. NEP-MST: Market Microstructure (7) 2014-12-19 2016-01-29 2016-04-23 2016-11-20 2017-01-08 2017-01-22 2017-07-16. Author is listed
  2. NEP-CMP: Computational Economics (5) 2010-12-23 2011-05-14 2015-05-30 2016-01-29 2017-01-22. Author is listed
  3. NEP-RMG: Risk Management (5) 2010-12-23 2015-02-11 2015-06-13 2017-06-04 2018-11-12. Author is listed
  4. NEP-UPT: Utility Models & Prospect Theory (4) 2016-10-30 2016-12-11 2018-10-01 2018-11-19
  5. NEP-BAN: Banking (1) 2010-12-23
  6. NEP-DCM: Discrete Choice Models (1) 2017-06-04
  7. NEP-DGE: Dynamic General Equilibrium (1) 2018-11-19
  8. NEP-FMK: Financial Markets (1) 2015-06-13
  9. NEP-IAS: Insurance Economics (1) 2013-10-25
  10. NEP-SEA: South East Asia (1) 2016-11-20

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