Optimal Consumption and Investment Problem under 4/2-CIR Stochastic Hybrid Model
Optimal Consumption and Investment Problem under 4/2-CIR Stochastic Hybrid Model
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DOI：
10.3390/math11173695
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发表时间：
2023-08
期刊：
影响因子：
2.4
通讯作者：
Aiqin Ma;Cuiyun Zhang;Yubin Wang
中科院分区：
文献类型：
--
作者：
Aiqin Ma;Cuiyun Zhang;Yubin Wang
本文研究了期望效用最大化准则下的最优消费和投资问题。假设金融市场由一种风险资产和一种无风险资产组成，风险资产价格服从4/2 Cox-Ingersoll-Ross（CIR）随机混合模型。投资目标是通过最大化目标函数获得最优消费投资策略。在幂效用函数下，利用最优控制理论和相应的Hamilton-Jacobi-Bellman（HJB）方程，得到了最优消费投资策略的闭式表达式。最后，通过一个算例说明了模型参数对最优消费投资策略的影响。
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.