具有索赔相依的最优再保险与投资策略

Optimal Reinsurance and Investment Strategies with Claim Dependence

大量实证研究表明,未来索赔与历史索赔相关.基于外推偏差法,文章建立了未来索赔对历史索赔的相依性,给出了保费计算方式,进而建立了保险公司的盈余过程.为了规避索赔风险,考虑了再保险;为了增加财富,考虑了在金融市场投资.因此,保险公司的最优决策包含再保险的最优决策和投资的最优决策.利用随机控制理论建立了值函数满足的Hamilton-Jacobi-Bellman (HJB)方程和验证定理.进而,在期望效用框架下,导出了最优再保险和投资策略.同时得到了保险公司集中化和分散化的投资准则.最终,在理论和数值实验两方面详细分析了模型关键参数对最优再保险和投资策略的影响,得到了一些深刻的决策建议.

A large number of empirical studies have shown that future claims are correlated with historical claims.Based on the extrapolation method,this paper establishes the dependence of future claims on historical claims,presents the premium calculation method,and then establishes the surplus process of insurance company.In order to avoid the claim risks,reinsurance is considered;in order to increase wealth,investment in financial market is considered.Therefore,the optimal decision-marking of the insurance company includes the optimal decision-marking of reinsurance and the optimal decision-marking of investment.We establish the Hamilton-Jacobi-Bellman(HJB) equation of the value function and verification theorem by using stochastic control theory.Then,under the expected utility framework,the optimal reinsurance and investment strategies are derived.Meanwhile,the investment criteria of centralization and decentralization of the insurance company are obtained.Finally,the influence of the key parameters of the model on the optimal reinsurance and investment strategy is analyzed in detail in both theoretical and numerical experiments,and some profound decision-making suggestions are obtained.