指数保费准则下存在模糊厌恶的最优分红策略

Optimal dividend strategy with ambiguity aversion under exponential premium principle

在经典风险模型的基础上,考虑指数保费准则下的分红模型,研究当模型存在模糊性时的最优分红问题.假设分红策略是一个壁垒策略,且仅与盈余过程有关,利用扩散模型逼近经典风险模型,并利用动态规划原理得到了Hamilton-Jacobi-Bellman(HJB)方程,进而得到模型存在模糊性时的值函数表达式及最优分红边界.通过数值算例给出模糊厌恶系数和风险厌恶系数对最优分红边界的影响.

On the basis of the classical risk model,dividend model is considered under exponential premium principle,and the optimal dividend is studied when the model has ambiguity.Assuming that the dividend strategy is a barrier strategy and only related to the surplus process,the diffusion model is used to approximate the classical risk model,and the Hamilton-Jacobi-Bellman equation is obtained by using the principle of dynamic programming.Then the value function and the optimal dividend boundary are obtained when the model has ambiguity.The influences of ambiguity aversion coefficient and risk aversion coefficient on the optimal dividend boundary are given through a numerical example.