常利息力影响下跳扩散模型的分红问题(英文)

Dividend Payments in Jump-Diffusion Risk Modelwith Interest and Constant Dividend Barrier

本文中用常值利率驱动下的经典跳扩散模型模拟保险公司的盈余过程,研究了该模型在带壁分红策略下的若干问题.首先得出破产前分红折现的高阶矩所满足的积分微分方程,并在指数分布的情况下借助合流超几何函数给出了方程的显式解.其次关于破产前聚合分红得到了一些令人满意的结果,这些结果甚至对一般的分布都成立,另外讨论了分红流的次数和额度.最后研究了指数分布时破产赤字折现期望问题.本文的部分结论深化了精算学中一些已有研究成果.

This article considers the compound Poisson insurance risk model perturbed by diffusion with investment and constant dividend barrier. Integro-differential equations for the high order moments of the discounted dividend payments prior to ruin are derived. Closed form solutions are formulated when the individual claim amount distribution is exponential. Some satisfying results about the distribution of the aggregate dividend are obtained, even for general claim size distributions. We also investigate the number and the amount of the dividend streams. Both the time of ruin and the deficit at ruin are considered in some special cases. Confluent hypergeometric functions play a key role in this paper.