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Portfolio Optimization with Delay Factor Models

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  • Shuenn-Jyi Sheu
  • Li-Hsien Sun
  • Zheng Zhang

Abstract

We propose an optimal portfolio problem in the incomplete market where the underlying assets depend on economic factors with delayed effects, such models can describe the short term forecasting and the interaction with time lag among different financial markets. The delay phenomenon can be recognized as the integral type and the pointwise type. The optimal strategy is identified through maximizing the power utility. Due to the delay leading to the non-Markovian structure, the conventional Hamilton-Jacobi-Bellman (HJB) approach is no longer applicable. By using the stochastic maximum principle, we argue that the optimal strategy can be characterized by the solutions of a decoupled quadratic forward-backward stochastic differential equations(QFBSDEs). The optimality is verified via the super-martingale argument. The existence and uniqueness of the solution to the QFBSDEs are established. In addition, if the market is complete, we also provide a martingale based method to solve our portfolio optimization problem, and investigate its connection with the proposed FBSDE approach. Finally, two particular cases are analyzed where the corresponding FBSDEs can be solved explicitly.

Suggested Citation

  • Shuenn-Jyi Sheu & Li-Hsien Sun & Zheng Zhang, 2018. "Portfolio Optimization with Delay Factor Models," Papers 1805.01118, arXiv.org.
    • Handle: RePEc:arx:papers:1805.01118
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    References listed on IDEAS

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    1. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    2. F. Gozzi & C. Marinelli & S. Savin, 2009. "On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 291-321, August.
    3. Belkacem Berdjane & Serguei Pergamenshchikov, 2013. "Optimal consumption and investment for markets with random coefficients," Finance and Stochastics, Springer, vol. 17(2), pages 419-446, April.
    4. {L}ukasz Delong & Claudia Kluppelberg, 2008. "Optimal investment and consumption in a Black--Scholes market with L\'evy-driven stochastic coefficients," Papers 0806.2570, arXiv.org.
    5. Rene Carmona & Jean-Pierre Fouque & Seyyed Mostafa Mousavi & Li-Hsien Sun, 2016. "Systemic Risk and Stochastic Games with Delay," Papers 1607.06373, arXiv.org.
    6. Giuliano Lorenzoni & Adrian Pizzinga & Rodrigo Atherino & Cristiano Fernandes & Rosane Riera Freire, 2007. "On the Statistical Validation of Technical Analysis," Brazilian Review of Finance, Brazilian Society of Finance, vol. 5(1), pages 3-28.
    7. 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.
    8. Nikolai Dokuchaev, 2015. "Modelling Possibility of Short-Term Forecasting of Market Parameters for Portfolio Selection," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 143-161, May.
    9. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    10. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
    11. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
    12. Po-Hsuan Hsu & Chung-Ming Kuan, 2005. "Reexamining the Profitability of Technical Analysis with Data Snooping Checks," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 606-628.
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    Cited by:

    1. Ying Zhao & Hui Mi & Lixia Xu, 2022. "Robust Optimal Investment Problem with Delay under Heston’s Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1271-1296, June.

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