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Robust Optimal Investment Problem with Delay under Heston’s Model

Author

Listed:
  • Ying Zhao

    (Nanjing Normal University)

  • Hui Mi

    (Nanjing Normal University)

  • Lixia Xu

    (Nanjing University of Finance and Economics)

Abstract

This paper considers a robust optimal portfolio problem under Heston model in which the risky asset price is related to the historical performance. The finance market includes a riskless asset and a risky asset whose price is controlled by a stochastic delay equation. The objective is to choose the investment strategy to maximize the minimal expected utility of terminal wealth. By employing dynamic programming principle and Hamilton-Jacobin-Bellman (HJB) equation, we obtain the specific expression of the optimal control and the explicit solution of the corresponding HJB equation. Besides, a verification theorem is provided to ensure the value function is indeed the solution of the HJB equation. Finally, we use numerical examples to illustrate the relationship between the optimal strategy and parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09885-3
    DOI: 10.1007/s11009-021-09885-3
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    References listed on IDEAS

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