两个合作保险公司的最优分红问题

Optimal Dividend Problem for Two Collaborating Insurance Companies

本文考虑两个均具复合泊松盈余过程的保险公司二维最优分红问题.在该模型中,余额过程为逐段决定马氏过程(PDMP),因此可借助PDMP及半动力系统可加泛函等理论研究最优分红问题.在得到最优值函数的性质后,我们给出可行策略与马氏策略的定义,并给出一个策略是平稳马氏策略的充分必要条件.然后运用测度值生成元理论得到测度值动态规划方程(测度值DPE),并在最优策略存在的前提下给出验证定理的证明.

In this paper,we consider the two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes.The surplus process is a piecewise deterministic Markov process(PDMP),so the optimal dividend problem can be studied by virtue of use the PDMP theory.After getting the properties of the optimal value function,we give the definition of admissible strategy and Markov strategy,and prove the necessary and sufficient condition for a strategy to be a stationary Markov strategy.Using the theory of measure-valued generators,we derive the associated measure-valued dynamic programming equation(measure-valued DPE).Finally we prove the verification theorem under the existence of the optimal strategy.