Reinsurance-investment game between two mean-variance insurers under model uncertainty
Reinsurance-investment game between two mean-variance insurers under model uncertainty
复制标题
模型不确定性下两家均值方差保险公司之间的再保险投资博弈
DOI：
10.1016/j.cam.2020.113095
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发表时间：
2021
影响因子：
2.4
通讯作者：
Linyi Qian
中科院分区：
文献类型：
--
作者：
Ning Wang;Nan Zhang;Zhuo Jin;Linyi Qian
摘要本文研究了时间一致均值方差准则下两个保险商之间的鲁棒非零和再保险投资随机微分对策。我们允许每个保险人购买比例再保险合同，并将其盈余投资于一个由一种无风险资产和一种风险资产组成的金融市场，以管理其保险风险。两个保险公司的盈余过程都服从经典的Cramer-Lundberg模型，每个保险公司都是一个模糊厌恶的保险公司（AAI），他们关注模型的不确定性。每个保险公司的目标是最大化相对于其竞争对手的预期终端盈余，并在替代措施的最坏情况下最小化该相对终端盈余的方差。应用随机控制理论中的技术，我们得到了扩展的Hamilton-Jacobi-Bellman（HJB）方程的保险公司。在复合Poisson风险模型及其扩散近似模型下，通过求解扩展的HJB方程，建立了保险公司的鲁棒均衡再保险投资策略和相应的均衡值函数.最后，我们进行了一些数值例子来说明几个模型参数的纳什均衡策略的影响。
Abstract This paper investigates a class of robust non-zero-sum reinsurance-investment stochastic differential games between two competing insurers under the time-consistent mean–variance criterion. We allow each insurer to purchase a proportional reinsurance treaty and invest his surplus into a financial market consisting of one risk-free asset and one risky asset to manage his insurance risk. The surplus processes of both insurers are governed by the classical Cramer-Lundberg model and each insurer is an ambiguity-averse insurer (AAI) who concerns about model uncertainty. The objective of each insurer is to maximize the expected terminal surplus relative to that of his competitor and minimize the variance of this relative terminal surplus under the worst-case scenario of alternative measures. Applying techniques in stochastic control theory, we obtain the extended Hamilton–Jacobi-Bellman (HJB) equations for both insurers. We establish the robust equilibrium reinsurance-investment strategies and the corresponding equilibrium value functions of both insurers by solving the extended HJB equations under both the compound Poisson risk model and its diffusion-approximated model. Finally, we conduct some numerical examples to illustrate the effects of several model parameters on the Nash equilibrium strategies.