具有共同冲击和错误定价的最优再保险与投资策略

Optimal Reinsurance and Investment Strategies with Common Shocks and Mispricing

摘要: 本文考虑了在错误定价模型下具有有限记忆和共同冲击的保险公司的最优再保险和投资策略问题。假设保险公司使用具有共同冲击依赖性的二维泊松过程来描述盈余过程，允许保险公司购买比例再保险且在金融市场进行投资来分散其风险。金融市场由无风险资产，市场指数和一对错误定价的股票组成。然后，在考虑与业绩相关的资本流入/流出的情况下，采用随机时滞微分方程来描述保险公司的财富过程。保险公司的目标是最大化终端财富和平均绩效财富组合的均值–方差效用，应用博弈论框架内的带时滞的随机控制理论，得到了最优再保险和投资策略的解析表达式。最后，通过数值例子对模型参数进行了敏感性分析。

Abstract: This paper considers the problem of optimal reinsurance and investment strategies for insurance companies with limited memory and common shocks under the mispricing model. Assume that insurers use a two-dimensional Poisson process with common shock dependence to describe the surplus process, allowing insurers to purchase proportional reinsurance and invest in financial markets to diversify their risk. Financial markets are made up of risk-free assets, market indices and a pair of mispriced stocks. Then, taking into account performance-related capital inflows/outflows, stochastic delay differential equations are used to describe the wealth process of insurance companies. The objective of insurance company is to maximize the mean-variance utility of the combination of terminal wealth and average performance wealth. The analytical expressions of optimal reinsurance and investment strategies are obtained by using stochastic control theory with time delay within the framework of game theory. Finally, a numerical example is given to analyze the sensitivity of the model parameters.