IDEAS home Printed from https://ideas.repec.org/a/bpj/jossai/v6y2018i1p35-57n3.html

Worst-Case Investment Strategy with Delay

Author

Listed:
  • A Chunxiang

    (School of Mathematics and Statistics, Zhaoqing University, Guangdong, 526061, China)

  • Shao Yi

    (School of Mathematics and Statistics, Zhaoqing University, Guangdong, 526061, China)

Abstract

This paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state (crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.

Suggested Citation

  • A Chunxiang & Shao Yi, 2018. "Worst-Case Investment Strategy with Delay," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 35-57, February.
    • Handle: RePEc:bpj:jossai:v:6:y:2018:i:1:p:35-57:n:3
    DOI: 10.21078/JSSI-2018-035-23
    as

    Download full text from publisher

    File URL: https://doi.org/10.21078/JSSI-2018-035-23
    Download Restriction: no
    File URL: https://libkey.io/10.21078/JSSI-2018-035-23?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    2. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. Lee, Min-Ku & Kim, Jeong-Hoon & Kim, Joocheol, 2011. "A delay financial model with stochastic volatility; martingale method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(16), pages 2909-2919.
    5. William N. Goetzmann & Jonathan E. Ingersoll & Stephen A. Ross, 2003. "High‐Water Marks and Hedge Fund Management Contracts," Journal of Finance, American Finance Association, vol. 58(4), pages 1685-1718, August.
    6. A, Chunxiang & Li, Zhongfei, 2015. "Optimal investment and excess-of-loss reinsurance problem with delay for an insurer under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 181-196.
    7. Ralf Korn & Olaf Menkens, 2005. "Worst-Case Scenario Portfolio Optimization: a New Stochastic Control Approach," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(1), pages 123-140, September.
    8. Mou-Hsiung Chang & Tao Pang & Yipeng Yang, 2011. "A Stochastic Portfolio Optimization Model with Bounded Memory," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 604-619, November.
    9. Frank Thomas Seifried, 2010. "Optimal Investment for Worst-Case Crash Scenarios: A Martingale Approach," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 559-579, August.
    10. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    11. Ralf Korn & Paul Wilmott, 2002. "Optimal Portfolios Under The Threat Of A Crash," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 171-187.
    12. Stavros Panageas & Mark M. Westerfield, 2009. "High‐Water Marks: High Risk Appetites? Convex Compensation, Long Horizons, and Portfolio Choice," Journal of Finance, American Finance Association, vol. 64(1), pages 1-36, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Belak, Christoph & Christensen, Sören & Menkens, Olaf, 2014. "Worst-case optimal investment with a random number of crashes," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 140-148.
    2. Frank Thomas Seifried, 2010. "Optimal Investment for Worst-Case Crash Scenarios: A Martingale Approach," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 559-579, August.
    3. Engler, Tina & Korn, Ralf, 2014. "Worst-case portfolio optimization under stochastic interest rate risk," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 2(4), pages 469-488.
    4. Lihua Chen & Ralf Korn, 2019. "Worst-case portfolio optimization in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(2), pages 197-227, October.
    5. Tina Engler & Ralf Korn, 2014. "Worst-Case Portfolio Optimization under Stochastic Interest Rate Risk," Risks, MDPI, vol. 2(4), pages 1-20, December.
    6. Kerstin Dächert & Ria Grindel & Elisabeth Leoff & Jonas Mahnkopp & Florian Schirra & Jörg Wenzel, 2022. "Multicriteria asset allocation in practice," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 349-373, June.
    7. Christensen, Bent Jesper & Parra-Alvarez, Juan Carlos & Serrano, Rafael, 2021. "Optimal control of investment, premium and deductible for a non-life insurance company," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 384-405.
    8. Nicole Branger & Matthias Muck & Stefan Weisheit, 2019. "Correlation risk and international portfolio choice," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 128-146, January.
    9. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    10. Ewald, Christian-Oliver & Zhang, Hai, 2016. "Hedge fund seeding via fees-for-seed swaps under idiosyncratic risk," Journal of Economic Dynamics and Control, Elsevier, vol. 71(C), pages 45-59.
    11. Rytchkov, Oleg, 2016. "Time-Varying Margin Requirements and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 51(2), pages 655-683, April.
    12. Chenxu Li & O. Scaillet & Yiwen Shen, 2020. "Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets," Swiss Finance Institute Research Paper Series 20-22, Swiss Finance Institute.
    13. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    14. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    15. Yiwen Shen & Chenxu Li & Olivier Scaillet & Yueting Jiang, 2026. "Dynamic Portfolio Allocation Under Market Incompleteness and Wealth Effects," Operations Research, INFORMS, vol. 74(1), pages 93-117, January.
    16. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2006. "Portfolio implications of systemic crises," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2347-2369, August.
    17. Anna Battauz & Alessandro Sbuelz, 2018. "Non†myopic portfolio choice with unpredictable returns: The jump†to†default case," European Financial Management, European Financial Management Association, vol. 24(2), pages 192-208, March.
    18. Stylianos Perrakis, 2022. "From innovation to obfuscation: continuous time finance fifty years later," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(3), pages 369-401, September.
    19. Marcos Escobar-Anel & Vincent Höhn & Luis Seco & Rudi Zagst, 2018. "Optimal fee structures in hedge funds," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 522-542, December.
    20. Marius Ascheberg & Nicole Branger & Holger Kraft & Frank Thomas Seifried, 2016. "When do jumps matter for portfolio optimization?," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1297-1311, August.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jossai:v:6:y:2018:i:1:p:35-57:n:3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyterbrill.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.