基于混合跳扩散模型的最优投资消费和寿险购买策略研究

doi:10.12005/orms.2021.0055

运筹与管理 ›› 2021, Vol. 30 ›› Issue (2): 155-161.DOI: 10.12005/orms.2021.0055

基于混合跳扩散模型的最优投资消费和寿险购买策略研究

杨朝强¹, 田有功²

1.兰州财经大学图书馆,甘肃兰州 730101;
2.兰州财经大学信息工程学院,甘肃兰州 730020

收稿日期:2019-01-06 出版日期:2021-02-25
作者简介:杨朝强(1984-),男,甘肃通渭人,学科馆员,硕士,研究方向:金融数学与金融工程;田有功(1977-),男,甘肃金昌人,副教授,博士,研究方向:风险管理与行为决策理论。
基金资助:
甘肃省高等学校创新基金项目(2020B-138);兰州财经大学科研项目(Lzufe2019C-009,Lzufe2017C-09)

Optimal Strategy of Life Insurance Investment and Consumption in Mixed Jump Diffusion Model

YANG Zhao-qiang¹, TIAN You-gong²

1. Library, Lanzhou University of Finance and Economics, Lanzhou 730101, China;
2. School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou 730020, China

Received:2019-01-06 Online:2021-02-25

摘要/Abstract

摘要： 本文研究在混合跳扩散模型下投资者分别投资于寿险、零息债券和股票时,关于最优投资消费和寿险购买的随机策略问题。通过构造满足混合跳扩散模型的金融市场、保险市场和可容许策略,在CRRA(constant relative risk aversion)效用下,利用动态规划的方法求解了对应的HJB方程,获得了值函数和最优策略的显式表达式。为了探索模型的有效性,本文给出了相对风险厌恶系数的数值分析以及相关参数对最优策略的影响。

关键词: 混合跳—扩散分数布朗运动, 人寿保险, CRRA效用, HJB方程, 最优策略, 数值分析

Abstract: In this paper, we consider the stochastic optimal strategy of consumption and investment when the investors invest in life insurance, zero coupon bonds and stock respectively under the mixed jump diffusion model, who have CRRA(constant relative risk aversion)preferences. By constructing the financial market, insurance market and admissible strategy to meet the mixed jump diffusion model, the HJB equation which is associated with the optimal strategy is solved by dynamic programming method. Then the explicit expression of the value function and the explicit expression of the optimal strategy are derived. To illustrate the validity of our model, the simulation of the relative risk aversion coefficient and the numerical analysis of the optimal parameters are also given.

Key words: mixed jump-diffusion fractional Brownian motion, life insurance, CRRA utility, HJB equation, optimal strategy, numerical analysis

中图分类号:

杨朝强, 田有功. 基于混合跳扩散模型的最优投资消费和寿险购买策略研究[J]. 运筹与管理, 2021, 30(2): 155-161.

YANG Zhao-qiang, TIAN You-gong. Optimal Strategy of Life Insurance Investment and Consumption in Mixed Jump Diffusion Model[J]. Operations Research and Management Science, 2021, 30(2): 155-161.

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基于混合跳扩散模型的最优投资消费和寿险购买策略研究

Optimal Strategy of Life Insurance Investment and Consumption in Mixed Jump Diffusion Model

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