一类双层非零和随机微分投资与再保险博弈模型

A Class of Hybrid Non-Zero-Sum Stochastic Differential Investment and Reinsurance Games

随着经济周期的变化,金融市场往往呈现出不同趋势状态之间的交替跳变,学术界常用马尔科夫机制转换模型来描述这一变化性质.针对马尔科夫机制转换模型下的金融投资市场,通过构建双层随机微分博弈模型,研究了一家再保险公司和两家保险公司之间的均衡投资与比例再保险策略问题.运用微分博弈理论和随机最优控制理论求解Hamilton Jacobi-Bellman方程,得到了均衡再保险和投资策略以及相应的值函数的解析表达.最后,通过数值算例研究了模型参数对均衡策略的影响,并分析了其背后的经济意义.

With the change of the economic cycle,financial markets often exhibit alternating transitions between different trend states,which is often described by the Markovian regime-switching model.Focusing on the financial investment market under the Markovian regime-switching model,this paper studies the equilibrium investment and proportional reinsurance strategies between a reinsurer and two insurers by constructing a two-level stochastic differential game model.By applying the differential game theory and stochastic optimal control approach,we derive the HJB equation for the value function.Meanwhile,we obtain analytical solutions to the value function and Nash equilibrium for equilibrium investment and reinsurance strategies.Finally,we provide numerical simulations together with economic implications.