运筹学学报 >
2021 , Vol. 25 >Issue 2: 35 - 54
DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2021.02.003
考虑时滞效应与均值-方差效用的非零和投资与再保险博弈
收稿日期: 2019-12-05
网络出版日期: 2021-05-06
基金资助
国家自然科学基金(71940012);广东省自然科学基金(2018A030313687)
Non-zero-sum investment and reinsurance game with delay effect and mean-variance utility
Received date: 2019-12-05
Online published: 2021-05-06
在考虑时滞效应的影响下研究了非零和随机微分投资与再保险博弈问题。以最大化终端绝对财富和相对财富的均值-方差效用为目标，构建了两个相互竞争的保险公司之间的非零和投资与再保险博弈模型，分别在经典风险模型和近似扩散风险模型下探讨了博弈的Nash均衡策略。借助随机控制理论以及相应的广义Hamilton-Jacobi-Bellman（HJB）方程，得到了均衡投资与再保险策略和值函数的显式表达。最后，通过数值例子分析了模型中相关参数变动对均衡策略的影响。
关键词： 投资与再保险; 非零和博弈; 时滞效应; 均值-方差效用; 广义Hamilton-Jacobi-Bellman方程
朱怀念, 钟慧, 宾宁 . 考虑时滞效应与均值-方差效用的非零和投资与再保险博弈[J]. 运筹学学报, 2021 , 25(2) : 35 -54 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.02.003
This paper investigates a non-zero-sum stochastic differential investment and reinsurance game with delay effect between two competitive insurers, who aim to maximize the mean-variance utility of his terminal wealth relative to that of his competitor. By applying stochastic control theory, corresponding extended Hamilton-Jacobi-Bellman (HJB) system of equations are established. Furthermore, closed-form expressions for the Nash equilibrium investment and reinsurance strategies and the corresponding value functions are derived both in the classical risk model and its diffusion approximation. Finally, some numerical examples are conducted to illustrate the influence of model parameters on the equilibrium investment and reinsurance strategies and draw some economic interpretations from these results.
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