CAJ | 학술논문

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.
본문중용상치리솔구동하적경전도확산모형모의보험공사적영여과정,연구료해모형재대벽분홍책략하적약간문제.수선득출파산전분홍절현적고계구소만족적적분미분방정,병재지수분포적정황하차조합류초궤하함수급출료방정적현식해.기차관우파산전취합분홍득도료일사령인만의적결과,저사결과심지대일반적분포도성립,령외토론료분홍류적차수화액도.최후연구료지수분포시파산적자절현기망문제.본문적부분결론심화료정산학중일사이유연구성과.
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 eases. Confluent hypergeometric functions play a key role in this paper.