均值-方差框架下保险公司和再保险公司的 Stackelberg 随机微分博弈

摘要/Abstract

摘要：

该文研究保险公司和再保险公司在 Heston 随机波动率风险模型中基于 Stackelberg 随机微分博弈框架下的最优投资再保险问题. 假定保险公司的索赔过程由泊松跳模型来描述, 通过期望值保费原则计算保费, 保险公司购买比例再保险将部分风险转移给再保险公司, 再保险公司接受转移的风险并选择合适的再保费策略, 保险公司和再保险公司还可将盈余投资于无风险资产和 Heston 随机波动率风险模型中. 以最大化终端财富值的均值-方差效用为目标, 利用随机控制理论建立相应的扩展 Hamilton-Jacobi-Bellman 方程, 给出验证定理, 得到均衡策略和值函数的具体形式, 最后通过数值模拟分析了模型参数对均衡策略的影响.

关键词: 均值-方差准则, 投资再保险策略, Heston 随机波动率, Stackelberg 随机微分博弈, 扩展 Hamilton-Jacobi-Bellman 方程

Abstract:

This paper studies the optimal reinsurance-investment problem of an insurer and a reinsurer under Heston's stochastic volatility model in the framework of Stackelberg stochastic differential game. We assume that the insurer purchases proportional reinsurance to transfer part of the risk to the reinsurer, and the reinsurer accepts the transferred risk and chooses an appropriate reinsurance premium strategy. At the same time, the insurer and the reinsurer can also invest their surplus in risk-free assets and Heston's stochastic volatility risk model. Under the criterion of maximizing the expected mean-variance utility of terminal wealth, the corresponding extended Hamilton-Jacobi-Bellman equations are developed using stochastic control theory, and verification theorems are given. We obtain specific forms for the equilibrium strategy and the value function. Finally, we analyze the effects of the model parameters on the equilibrium strategies through numerical simulations.

Key words: mean-variance criterion, reinsurance and investment strategy, Heston's SV, Stackelberg stochastic differential game, extended Hamilton-Jacobi-Bellman equation

中图分类号:

O211.6

温玉珍, 王绍琳. 均值-方差框架下保险公司和再保险公司的 Stackelberg 随机微分博弈[J]. 数学物理学报, 2025, 45(4): 1327-1353.

Wen Yuzhen, Wang Shaolin. Stackelberg Stochastic Differential Game of Insurer and Reinsurer Under Mean-Variance Framework[J]. Acta mathematica scientia,Series A, 2025, 45(4): 1327-1353.

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