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Tommi Sottinen

Personal Details

First Name:Tommi
Middle Name:
Last Name:Sottinen
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RePEc Short-ID:pso44
http://www.uwasa.fi/~tsottine/
Tommi Sottinen University of Vaasa Faculty of Technology Department of Mathematics and Statistics P.O.Box 700 FIN-65101 Vaasa FINLAND

Affiliation

Vaasan yliopisto, Matemaattisten tieteiden laitos (University of Vaasa, Department of Mathematics and Statistics)

http://www.uwasa.fi/matemaattiset/english/
Finland, Vaasa

Research output

as
Jump to: Working papers Articles

Working papers

  1. Tommi Sottinen & Adil Yazigi, 2012. "Generalized Gaussian Bridges," Papers 1205.3405, arXiv.org, revised Nov 2013.
  2. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.

Articles

  1. Pakkanen, Mikko S. & Sottinen, Tommi & Yazigi, Adil, 2017. "On the conditional small ball property of multivariate Lévy-driven moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 749-782.
  2. Azmoodeh, Ehsan & Sottinen, Tommi & Viitasaari, Lauri & Yazigi, Adil, 2014. "Necessary and sufficient conditions for Hölder continuity of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 230-235.
  3. Sottinen, Tommi & Yazigi, Adil, 2014. "Generalized Gaussian bridges," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3084-3105.
  4. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.
  5. Tommi Sottinen & Ciprian Tudor, 2008. "Parameter estimation for stochastic equations with additive fractional Brownian sheet," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 221-236, October.
  6. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
  7. Sottinen Tommi & Valkeila Esko, 2003. "On arbitrage and replication in the fractional Black–Scholes pricing model," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 93-108, February.
  8. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.

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. Tommi Sottinen & Adil Yazigi, 2012. "Generalized Gaussian Bridges," Papers 1205.3405, arXiv.org, revised Nov 2013.

    Cited by:

    1. Sottinen, Tommi & Viitasaari, Lauri, 2017. "Prediction law of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 155-166.

  2. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.

    Cited by:

    1. Fernando Cordero & Lavinia Perez-Ostafe, 2014. "Critical transaction costs and 1-step asymptotic arbitrage in fractional binary markets," Papers 1407.8068, arXiv.org.
    2. Benjamín Vallejo Jiménez & Francisco Venegas Martínez, 2017. "Optimal consumption and portfolio rules when the asset price is driven by a time-inhomogeneous Markov modulated fractional Brownian motion with," Economics Bulletin, AccessEcon, vol. 37(1), pages 314-326.
    3. Sebastian E. Ferrando & Alfredo L. Gonzalez & Ivan L. Degano & Massoome Rahsepar, 2014. "Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals," Papers 1407.1769, arXiv.org, revised Nov 2015.
    4. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2017. "Pricing derivatives in Hermite markets," Papers 1709.09068, arXiv.org.
    5. Hasanjan Sayit, 2013. "Absence of arbitrage in a general framework," Annals of Finance, Springer, vol. 9(4), pages 611-624, November.
    6. Mishura, Yuliya & Shevchenko, Georgiy & Valkeila, Esko, 2013. "Random variables as pathwise integrals with respect to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2353-2369.
    7. Alexander Schied, 2013. "Model-free CPPI," Papers 1305.5915, arXiv.org, revised Jan 2014.
    8. Ehsan Azmoodeh, 2010. "On the fractional Black-Scholes market with transaction costs," Papers 1005.0211, arXiv.org.
    9. Foad Shokrollahi & Tommi Sottinen, 2017. "Hedging in fractional Black-Scholes model with transaction costs," Papers 1706.01534, arXiv.org, revised Jul 2017.
    10. Christian Bender, 2012. "Simple arbitrage," Papers 1210.5391, arXiv.org.
    11. Nikolai Dokuchaev, 2015. "On the no-arbitrage market and continuity in the Hurst parameter," Papers 1509.06472, arXiv.org, revised Oct 2015.

Articles

  1. Azmoodeh, Ehsan & Sottinen, Tommi & Viitasaari, Lauri & Yazigi, Adil, 2014. "Necessary and sufficient conditions for Hölder continuity of Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 230-235.

    Cited by:

    1. Sottinen, Tommi & Viitasaari, Lauri, 2017. "Prediction law of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 155-166.

  2. Sottinen, Tommi & Yazigi, Adil, 2014. "Generalized Gaussian bridges," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3084-3105.
    See citations under working paper version above.
  3. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.

    Cited by:

    1. Shokrollahi, Foad & Sottinen, Tommi, 2017. "Hedging in fractional Black–Scholes model with transaction costs," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 85-91.
    2. Foad Shokrollahi & Tommi Sottinen, 2017. "Hedging in fractional Black-Scholes model with transaction costs," Papers 1706.01534, arXiv.org, revised Jul 2017.
    3. Tommi Sottinen & Lauri Viitasaari, 2017. "Conditional-Mean Hedging Under Transaction Costs in Gaussian Models," Papers 1708.03242, arXiv.org.

  4. Tommi Sottinen & Ciprian Tudor, 2008. "Parameter estimation for stochastic equations with additive fractional Brownian sheet," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 221-236, October.

    Cited by:

    1. Bertin, Karine & Torres, Soledad & Tudor, Ciprian A., 2011. "Drift parameter estimation in fractional diffusions driven by perturbed random walks," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 243-249, February.
    2. Nenghui Kuang & Huantian Xie, 2015. "Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 75-91, February.

  5. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.

    Cited by:

    1. Alexander Schied & Iryna Voloshchenko, 2015. "Pathwise no-arbitrage in a class of Delta hedging strategies," Papers 1511.00026, arXiv.org, revised Jun 2016.
    2. Ehsan Azmoodeh & Esko Valkeila, 2013. "Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 97-112, July.
    3. Xiao, Weilin & Zhang, Weiguo & Xu, Weijun & Zhang, Xili, 2012. "The valuation of equity warrants in a fractional Brownian environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1742-1752.
    4. Erhan Bayraktar & Mikko S. Pakkanen & Hasanjan Sayit, 2009. "On the Existence of Consistent Price Systems," Papers 0911.3789, arXiv.org, revised Jun 2013.
    5. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    6. Andreas Neuenkirch & Samy Tindel, 2014. "A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 99-120, April.
    7. Schied, Alexander, 2014. "Model-free CPPI," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 84-94.
    8. Holger Fink, 2016. "Conditional Distributions of Mandelbrot–van ness Fractional LÉVY Processes and Continuous-Time ARMA–GARCH-Type Models with Long Memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 30-45, January.
    9. Svetlozar Rachev & Frank Fabozzi, 2016. "Financial market with no riskless (safe) asset," Papers 1612.02112, arXiv.org.
    10. Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
    11. Cristina Di Girolami & Giorgio Fabbri & Francesco Russo, 2013. "The covariation for Banach space valued processes and applications," Documents de recherche 13-01, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    12. Frank Riedel, 2015. "Financial economics without probabilistic prior assumptions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 75-91, April.
    13. Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 129-144, December.
    14. Jos'e Igor Morlanes, 2017. "Mixed Models as an Alternative to Farima," Papers 1712.03044, arXiv.org.
    15. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.
    16. Hasanjan Sayit, 2013. "Absence of arbitrage in a general framework," Annals of Finance, Springer, vol. 9(4), pages 611-624, November.
    17. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xili & Zhang, Xiaoli, 2012. "Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6418-6431.
    18. Alexander Schied, 2013. "Model-free CPPI," Papers 1305.5915, arXiv.org, revised Jan 2014.
    19. Alexander Alvarez & Sebastian E. Ferrando, 2016. "Trajectory-Based Models, Arbitrage And Continuity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-34, May.
    20. Rosanna Coviello & Cristina Di Girolami & Francesco Russo, 2011. "On stochastic calculus related to financial assets without semimartingales," Papers 1102.2050, arXiv.org.
    21. Pakkanen, Mikko S. & Sottinen, Tommi & Yazigi, Adil, 2017. "On the conditional small ball property of multivariate Lévy-driven moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 749-782.
    22. Alexander Schied, 2015. "On a class of generalized Takagi functions with linear pathwise quadratic variation," Papers 1501.00837, arXiv.org, revised Aug 2015.
    23. Alexander Alvarez & Sebastian Ferrando & Pablo Olivares, 2011. "Arbitrage and Hedging in a non probabilistic framework," Papers 1103.1006, arXiv.org.
    24. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xi-Li & Wang, Ying-Luo, 2010. "Pricing currency options in a fractional Brownian motion with jumps," Economic Modelling, Elsevier, vol. 27(5), pages 935-942, September.
    25. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    26. Christian Bender, 2012. "Simple arbitrage," Papers 1210.5391, arXiv.org.

  6. Sottinen Tommi & Valkeila Esko, 2003. "On arbitrage and replication in the fractional Black–Scholes pricing model," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 93-108, February.

    Cited by:

    1. Wang, Xiao-Tian, 2011. "Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black–Scholes model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1623-1634.
    2. Yamada, Toshihiro, 2015. "A formula of small time expansion for Young SDE driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 64-72.
    3. Xiao, Weilin & Zhang, Weiguo & Xu, Weijun & Zhang, Xili, 2012. "The valuation of equity warrants in a fractional Brownian environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1742-1752.
    4. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    5. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2017. "Pricing derivatives in Hermite markets," Papers 1709.09068, arXiv.org.
    6. Erhan Bayraktar & H. Vincent Poor & K. Ronnie Sircar, 2004. "Estimating The Fractal Dimension Of The S&P 500 Index Using Wavelet Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 615-643.
    7. Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 129-144, December.
    8. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19.
    9. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.
    10. Mikko S. Pakkanen & Jani Lukkarinen, 2016. "Arbitrage without borrowing or short selling?," CREATES Research Papers 2016-13, Department of Economics and Business Economics, Aarhus University.
    11. Wang, Xiao-Tian, 2010. "Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 438-444.
    12. Foad Shokrollahi, 2017. "The valuation of European option with transaction costs by mixed fractional Merton model," Papers 1702.00152, arXiv.org.
    13. Ehsan Azmoodeh, 2010. "On the fractional Black-Scholes market with transaction costs," Papers 1005.0211, arXiv.org.
    14. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    15. Jani Lukkarinen & Mikko S. Pakkanen, 2016. "Arbitrage without borrowing or short selling?," Papers 1604.07690, arXiv.org, revised Oct 2016.
    16. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    17. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
    18. Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.

  7. Tommi Sottinen, 2001. "Fractional Brownian motion, random walks and binary market models," Finance and Stochastics, Springer, vol. 5(3), pages 343-355.

    Cited by:

    1. Garzón, J. & Gorostiza, L.G. & León, J.A., 2009. "A strong uniform approximation of fractional Brownian motion by means of transport processes," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3435-3452, October.
    2. Fernando Cordero & Lavinia Perez-Ostafe, 2014. "Critical transaction costs and 1-step asymptotic arbitrage in fractional binary markets," Papers 1407.8068, arXiv.org.
    3. Nieminen, Ari, 2004. "Fractional Brownian motion and Martingale-differences," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 1-10, October.
    4. Gloter, A. & Hoffmann, M., 2004. "Stochastic volatility and fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 113(1), pages 143-172, September.
    5. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    6. R. Vilela Mendes & M. J. Oliveira & A. M. Rodrigues, 2012. "The fractional volatility model: No-arbitrage, leverage and completeness," Papers 1205.2866, arXiv.org.
    7. Nils Chr. Framstad, 2012. "On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes," Papers 1206.5756, arXiv.org, revised Jun 2012.
    8. Kubilius, K., 2008. "On the convergence of stochastic integrals with respect to p-semimartingales," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2528-2535, October.
    9. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2017. "Pricing derivatives in Hermite markets," Papers 1709.09068, arXiv.org.
    10. Power, Gabriel J. & Turvey, Calum G., 2010. "Long-range dependence in the volatility of commodity futures prices: Wavelet-based evidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 79-90.
    11. Bertin, Karine & Torres, Soledad & Tudor, Ciprian A., 2011. "Drift parameter estimation in fractional diffusions driven by perturbed random walks," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 243-249, February.
    12. Cordero, Fernando & Klein, Irene & Perez-Ostafe, Lavinia, 2016. "Asymptotic proportion of arbitrage points in fractional binary markets," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 315-336.
    13. Blanka Horvath & Antoine Jacquier & Aitor Muguruza, 2017. "Functional central limit theorems for rough volatility," Papers 1711.03078, arXiv.org, revised Nov 2017.
    14. Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 129-144, December.
    15. Bardina, X. & Nourdin, I. & Rovira, C. & Tindel, S., 2010. "Weak approximation of a fractional SDE," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 39-65, January.
    16. Daniel Conus & Mackenzie Wildman, 2016. "A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivatives," Papers 1608.03428, arXiv.org.
    17. Klüppelberg, Claudia & Kühn, Christoph, 2004. "Fractional Brownian motion as a weak limit of Poisson shot noise processes--with applications to finance," Stochastic Processes and their Applications, Elsevier, vol. 113(2), pages 333-351, October.
    18. Inoue, Akihiko & Nakano, Yumiharu & Anh, Vo, 2007. "Binary market models with memory," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 256-264, February.
    19. Gapeev Pavel V. & Sottinen Tommi & Valkeila Esko, 2011. "Robust replication in H-self-similar Gaussian market models under uncertainty," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 37-50, March.
    20. Slominski, Leszek & Ziemkiewicz, Bartosz, 2009. "On weak approximations of integrals with respect to fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 543-552, February.
    21. Zhang, Pu & Sun, Qi & Xiao, Wei-Lin, 2014. "Parameter identification in mixed Brownian–fractional Brownian motions using Powell's optimization algorithm," Economic Modelling, Elsevier, vol. 40(C), pages 314-319.
    22. Hasanjan Sayit, 2013. "Absence of arbitrage in a general framework," Annals of Finance, Springer, vol. 9(4), pages 611-624, November.
    23. Rostek, Stefan & Schöbel, Rainer, 2006. "Risk preference based option pricing in a fractional Brownian market," Tübinger Diskussionsbeiträge 299, University of Tübingen, School of Business and Economics.
    24. Giulia Rotundo & Roy Cerqueti, 2010. "Options With Underlying Asset Driven By A Fractional Brownian Motion: Crossing Barriers Estimates," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 109-118.
    25. Zhigang Tong, 2016. "Option pricing in stochastic volatility models driven by fractional Lévy processes," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 56-75.
    26. Hideharu Funahashi & Masaaki Kijima, 2017. "Does the Hurst index matter for option prices under fractional volatility?," Annals of Finance, Springer, vol. 13(1), pages 55-74, February.
    27. Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
    28. Turvey, Calum G., 2007. "A note on scaled variance ratio estimation of the Hurst exponent with application to agricultural commodity prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 155-165.
    29. Holger Fink & Christian Scherr, 2014. "CDS pricing with long memory via fractional Lévy processes," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-35.
    30. Fernando Cordero & Lavinia Perez-Ostafe, 2015. "Critical Transaction Costs And 1-Step Asymptotic Arbitrage In Fractional Binary Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-26.
    31. Sottinen Tommi & Valkeila Esko, 2003. "On arbitrage and replication in the fractional Black–Scholes pricing model," Statistics & Risk Modeling, De Gruyter, vol. 21(2/2003), pages 93-108, February.
    32. Nenghui Kuang & Huantian Xie, 2015. "Maximum likelihood estimator for the sub-fractional Brownian motion approximated by a random walk," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 75-91, February.
    33. Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2016. "Pricing Derivatives in Hermite Markets," Papers 1612.07016, arXiv.org, revised Dec 2016.
    34. Christian Bender & Tommi Sottinen & Esko Valkeila, 2010. "Fractional processes as models in stochastic finance," Papers 1004.3106, arXiv.org.
    35. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
    36. Vilela Mendes, R. & Oliveira, M.J. & Rodrigues, A.M., 2015. "No-arbitrage, leverage and completeness in a fractional volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 470-478.
    37. Hideharu Funahashi, 2017. "Pricing derivatives with fractional volatility," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-28, March.
    38. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.
    39. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.
    40. Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.
    41. Zhang, Pu & Xiao, Wei-lin & Zhang, Xi-li & Niu, Pan-qiang, 2014. "Parameter identification for fractional Ornstein–Uhlenbeck processes based on discrete observation," Economic Modelling, Elsevier, vol. 36(C), pages 198-203.

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