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Optimal Consumption and Investment Problem under 4/2-CIR Stochastic Hybrid Model

Author

Listed:
  • Aiqin Ma

    (School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China)

  • Cuiyun Zhang

    (School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China)

  • Yubing Wang

    (School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China)

Abstract

In this paper, we investigate the optimal consumption and investment problem under the expected utility maximization criterion. It is supposed that the financial market consists of a risky asset and a risk-free asset, and the risky asset prices follow the 4/2 Cox–Ingersoll–Ross (CIR) stochastic hybrid model. The investment objective is to obtain an optimal consumption–investment strategy by maximizing the objective function. The closed-form expression of the optimal consumption–investment strategy is obtained by using optimal control theory and the corresponding Hamilton–Jacobi–Bellman (HJB) equation under the power utility function. In addition, we present a numerical example to illustrate the influence of model parameters on the optimal consumption–investment strategy.

Suggested Citation

  • Aiqin Ma & Cuiyun Zhang & Yubing Wang, 2023. "Optimal Consumption and Investment Problem under 4/2-CIR Stochastic Hybrid Model," Mathematics, MDPI, vol. 11(17), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3695-:d:1226881
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    References listed on IDEAS

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