逐段决定复合泊松风险模型的最优分红策略

Optimal Dividend Strategy in the Piecewise-deterministic Compound Poisson Risk Model

基于逐段决定复合泊松风险模型,针对保险公司的最优红利分配问题进行研究,目标是破产前的累积分红折现均值与破产时的罚金支付之和最大化.在分红速率受限制的情况下,给出了值函数的HJB方程,经过验证定理推出值函数是相应HJB方程的最优解,从而证明了最优分红策略即为阀值策略.

Based on piecewise-determinist ic comp o u n d Poisson r is k mod e l t hi s paper concerns an o p t im a l dividend distribution problem wi th regard to an insurance c om p a n y .O u r object ive is to m a x im iz e the sum of the means of the cumulat ive discounted d iv idend payme n ts u n t i l ru in and a p e n al ty p a ym e n t at thetime of ruin.Then in the case of bounded d iv idend ra te , the paper presents e x p l ic i t ly the co rresponding Hamilton - Jacobi-Bellman equat ion wh ic h satisfies the o p t im a l value fu n c t io n . F u r th e rm o re ？ the value function is demonstrated to be a so lu t io n o f the associated H JB equat ion by ve r i f ic a t io n th e o rem , and it proves that the optimal dividend s tra te g y is the th re s h o ld s t ra te g y .