违约市场中的n个保险公司的最优投资和再保险问题  

OPTIMAL INVESTMENT-REINSURANCE PROBLEM FOR N INSURERS WITH A DEFAULTABLE SECURITY

作　　者：邢小玉[1] 高豪 于亚丽 李晓芳 XING Xiao-yu;GAO Hao;YU Ya-li;LI Xiao-fang(School of Science,Hebei University of Technology,Tianjin 300401,China)

机构地区：[1]河北工业大学理学院,天津300401

出　　处：《数学杂志》2022年第4期315-329,共15页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10271107)。

摘　　要：本文研究了n个保险公司之间的非零和随机微分投资再保险博弈问题.每个保险公司可以购买比例再保险,并将财富投资于一个由无风险资产,可违约债券和n个风险资产组成的金融市场.特别地,风险资产的价格过程服从CEV模型,可违约债券可在违约时收回一定比例的价值.每个保险公司的目标是相对于竞争对手,最大化终端财富的期望指数效用.利用随机最优控制理论,我们分别推导了均衡策略和均衡值函数的显式表达式.数值例子分析了模型参数对均衡策略的影响.此外,我们还分析了保险公司数量对均衡投资策略的影响.我们发现,随着保险公司数量的增加,每个保险公司将在风险资产和可违约债券上投入更多的资金.This paper considers a non-zero-sum stochastic differential investment-reinsurance game between n competitive insurers.Each insurer can purchase proportional reinsurance and trade in a more general financial market consisting of a risk-free asset,a defaultable bond and n risky assets.In particular,the risky asset’s price process is modeled by a constant elasticity of variance(CEV)model and the defaultable bond with proportional recovery at default.The objective of each insurer is to maximize the expected exponential utility of the terminal wealth relative to the competitors.By applying stochastic optimal control theory,the explicit expressions of equilibrium strategies and equilibrium value functions are derived,respectively.Numerical examples are given to illustrate the effects of parameters on the equilibrium policies,as well as,we examine how the number of insurers on the optimal equilibrium investment strategies.We find that when the number of insurers increases,each insurer will invest more money in risky assets and defaultable bond.

关 键 词：投资再保险 非零和博弈 可违约债券 指数效应函数 CEV模型 

分 类 号：O211.6[理学—概率论与数理统计] O29[理学—数学]