CAJ | 학술논문

本文研究随机保费风险模型下与破产时刻相关的平均折现罚金函数.与经典的Cramér-Lundberg模型相比这里的保费过程不再是时间的线性函数,而是一个与理赔独立的复合Possjon过程.我们得到了罚金函数所满足的积分方程,它提供了一种研究破产量的统一方法.利用该积分方程我们得到了破产时刻,破产时赤字,破产前瞬时盈余的Laplace变换;并在指数分布的特殊情况下求出了他们的显著表达式,推广了Boikov(2003)的结论.
본문연구수궤보비풍험모형하여파산시각상관적평균절현벌금함수.여경전적Cramér-Lundberg모형상비저리적보비과정불재시시간적선성함수,이시일개여리배독립적복합Possjon과정.아문득도료벌금함수소만족적적분방정,타제공료일충연구파산량적통일방법.이용해적분방정아문득도료파산시각,파산시적자,파산전순시영여적Laplace변환;병재지수분포적특수정황하구출료타문적현저표체식,추엄료Boikov(2003)적결론.
This paper studies the expected discounted penalty function associated with the time of ruin for a risk model with stochastic premium. The premium process is no longer a linear function of time in contrast with the classical Cramér-Lundberg model. The aggregate premiums constitute a compound Poisson process which is also independent of the claim process. Integral equation for the penalty function is derived, which provides a unified treatment to the ruin quantities. Applications of the integral equation are given to the Laplace transform of the time of ruin, the deficit at ruin, the surplus immediately before ruin occurs. In some special cases with exponential distributions, closed form expressions for these quantities are obtained, which generalize some known results about the problems of ruin in Boikov (2003).