复合二项风险模型下Gerber-Shiu折现惩罚函数的渐近解

AN ASYMPTOTIC RELATIONSHIP OF THE GERBER-SHIU DISCOUNT PENALTY FUNCTION IN THE COMPOUND BINOMIAL RISK MODEL

首先研究了二项风险模型下Gerber-Shiu折现惩罚函数所满足的瑕疵更新方程,然后根据离散更新方程理论研究了其渐近解,并得到了破产概率、破产即刻前赢余和破产时刻赤字的联合分布分布以及其边际分布等的渐近解,进一步完善了Pavlova K P和Willmot G E 2004年发表的相关问题的结果.

This paper considers the compound binomial risk model, studies the defective renewal equation satisfied by the Gerber-Shiu discount penalty function, and obtains the asymptotic relationship of the the Gerber-Shiu discount penalty function basied on the renewal theory. Furthermore, the asymptotic relationships of the joint distributions and the marginal distributions of the deficit at ruin and the surplus immediately prior to ruin are given. These results extend that obtained by Pavlova and Willmot in 2004.