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

Aiqin Ma (), Cuiyun Zhang and Yubing Wang
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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

Mathematics, 2023, vol. 11, issue 17, 1-19

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.

Keywords: 4/2 stochastic volatility; CIR interest rate; optimal strategy; CRRA utility; HJB equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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