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Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model

Author

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  • Ma, Jingtang
  • Li, Wenyuan
  • Zheng, Harry

Abstract

The aim of this paper is to study the fast computation of the lower and upper bounds on the value function for utility maximization under the Heston stochastic volatility model with general utility functions. It is well known there is a closed form solution to the HJB equation for power utility due to its homothetic property. It is not possible to get closed form solution for general utilities and there is little literature on the numerical scheme to solve the HJB equation for the Heston model. In this paper we propose an efficient dual control Monte-Carlo method for computing tight lower and upper bounds of the value function. We identify a particular form of the dual control which leads to the closed form upper bound for a class of utility functions, including power, non-HARA and Yaari utilities. Finally, we perform some numerical tests to see the efficiency, accuracy, and robustness of the method. The numerical results support strongly our proposed scheme.

Suggested Citation

  • Ma, Jingtang & Li, Wenyuan & Zheng, Harry, 2020. "Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 280(2), pages 428-440.
    • Handle: RePEc:eee:ejores:v:280:y:2020:i:2:p:428-440
    DOI: 10.1016/j.ejor.2019.07.041
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    Cited by:

    1. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    2. Ashley Davey & Harry Zheng, 2020. "Deep Learning for Constrained Utility Maximisation," Papers 2008.11757, arXiv.org, revised Aug 2021.
    3. Ewald, Christian Oliver & Nolan, Charles, 2024. "On the adaptation of the Lagrange formalism to continuous time stochastic optimal control: A Lagrange-Chow redux," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    4. Kristof Wiedermann, 2022. "An SMP-Based Algorithm for Solving the Constrained Utility Maximization Problem via Deep Learning," Papers 2202.07771, arXiv.org.
    5. Jingtang Ma & Zhengyang Lu & Zhenyu Cui, 2022. "Delta family approach for the stochastic control problems of utility maximization," Papers 2202.12745, arXiv.org.
    6. Ashley Davey & Harry Zheng, 2022. "Deep Learning for Constrained Utility Maximisation," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 661-692, June.

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