Markov调节中基于时滞和相依风险模型的最优再保险与投资

Optimal reinsurance and investment in a Markovian regime-switching economy with delay and common shock

本文研究保险公司在Markov调节下基于时滞及相依风险模型的最优再保险与最优投资问题,其中市场被划分为有限个状态,一些重要的参数随着市场状态的转换而变化.假设保险公司的盈余过程由复合Poisson过程描述,而风险资产的价格过程由几何跳扩散模型刻画,并且假设这两个跳过程是相依的.以最大化终端财富值的均值-方差效用为目标,在博弈论框架下,利用随机控制理论和相应的广义Hamilton-Jacobi-Bellman(HJB)方程,本文得到最优策略和值函数的显式表达,并证明解的存在性和唯一性.最后,通过一些数值实例,验证所得结论的正确性,并探讨一些重要参数对最优策略的影响.

This paper studies the optimal reinsurance and investment problem for an insurer in a Markovian regime-switching economy with the delayed system,in which the market modes are divided into a finite number of regimes,and all the key parameters change according to the value of different market modes.It is assumed that the insurance risk process of the insurer is modulated by a compound Poisson process while the price process of the risky asset is governed by a jump-diffusion model,and that the two jump processes are correlated through a common shock.Under the criterion of maximizing the expected mean-variance utility of terminal wealth,explicit expressions for the optimal strategies and the value function are obtained within a game theoretic framework by using the technique of stochastic control theory and the corresponding extended Hamilton-Jacobi-Bellman equation.The existence and uniqueness of the solutions are also verified.Finally,numerical examples are presented to show the impacts of some parameters on the optimal results.