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A Neural Network Monte Carlo Approximation for Expected Utility Theory

Author

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  • Yichen Zhu

    (Department of Statistical and Actuarial Sciences, Western University, London, ON N6A5B7, Canada
    These authors contributed equally to this work.)

  • Marcos Escobar-Anel

    (Department of Statistical and Actuarial Sciences, Western University, London, ON N6A5B7, Canada
    These authors contributed equally to this work.)

Abstract

This paper proposes an approximation method to create an optimal continuous-time portfolio strategy based on a combination of neural networks and Monte Carlo, named NNMC. This work is motivated by the increasing complexity of continuous-time models and stylized facts reported in the literature. We work within expected utility theory for portfolio selection with constant relative risk aversion utility. The method extends a recursive polynomial exponential approximation framework by adopting neural networks to fit the portfolio value function. We developed two network architectures and explored several activation functions. The methodology was applied on four settings: a 4/2 stochastic volatility (SV) model with two types of market price of risk, a 4/2 model with jumps, and an Ornstein–Uhlenbeck 4/2 model. In only one case, the closed-form solution was available, which helps for comparisons. We report the accuracy of the various settings in terms of optimal strategy, portfolio performance and computational efficiency, highlighting the potential of NNMC to tackle complex dynamic models.

Suggested Citation

  • Yichen Zhu & Marcos Escobar-Anel, 2021. "A Neural Network Monte Carlo Approximation for Expected Utility Theory," JRFM, MDPI, vol. 14(7), pages 1-18, July.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:7:p:322-:d:593076
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    References listed on IDEAS

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    1. Michael W. Brandt & Amit Goyal & Pedro Santa-Clara & Jonathan R. Stroud, 2005. "A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 831-873.
    2. Yuyang Cheng & Marcos Escobar-Anel, 2021. "Optimal investment strategy in the family of 4/2 stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(10), pages 1723-1751, October.
    3. Zhu, Yichen & Escobar-Anel, Marcos, 2022. "Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck 4/2 models," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    4. Fei Cong & Cornelis W. Oosterlee, 2017. "Accurate and Robust Numerical Methods for the Dynamic Portfolio Management Problem," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 433-458, March.
    5. Holger Kraft, 2005. "Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility," Quantitative Finance, Taylor & Francis Journals, vol. 5(3), pages 303-313.
    6. Jain, Shashi & Oosterlee, Cornelis W., 2015. "The Stochastic Grid Bundling Method: Efficient pricing of Bermudan options and their Greeks," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 412-431.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    8. Cvitanic, Jaksa & Goukasian, Levon & Zapatero, Fernando, 2003. "Monte Carlo computation of optimal portfolios in complete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 971-986, April.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    10. Jérôme B. Detemple & Ren Garcia & Marcel Rindisbacher, 2003. "A Monte Carlo Method for Optimal Portfolios," Journal of Finance, American Finance Association, vol. 58(1), pages 401-446, February.
    11. Christian Flor & Linda Larsen, 2014. "Robust portfolio choice with stochastic interest rates," Annals of Finance, Springer, vol. 10(2), pages 243-265, May.
    12. Chiu, Mei Choi & Wong, Hoi Ying, 2013. "Optimal investment for an insurer with cointegrated assets: CRRA utility," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 52-64.
    13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    14. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    15. Chen, Shun & Ge, Lei, 2021. "A learning-based strategy for portfolio selection," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 936-942.
    16. Marcos Escobar‐Anel & Zhenxian Gong, 2020. "The mean‐reverting 4/2 stochastic volatility model: Properties and financial applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(5), pages 836-856, September.
    17. 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.
    18. M. Escobar & D. Neykova & R. Zagst, 2017. "HARA utility maximization in a Markov-switching bond–stock market," Quantitative Finance, Taylor & Francis Journals, vol. 17(11), pages 1715-1733, November.
    19. Li, Yuying & Forsyth, Peter A., 2019. "A data-driven neural network approach to optimal asset allocation for target based defined contribution pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 189-204.
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