负二项(2)风险过程的Gerber-Shui罚金函数  

The Gerber-Shui Penalty Function in the Negative Binomial (2) Risk Process

作　　者：柏立华[1] 马建静 

机构地区：[1]南开大学数学科学学院,天津300071 [2]山东工商学院数学与信息学院,山东烟台264005

出　　处：《南开大学学报（自然科学版）》2007年第6期6-12,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(10571092)

摘　　要：考虑了负二项(2)风险过程的破产时刻被折现罚金的期望值,它是一个关于初始余额的函数,即 Ger-ber-Shui 罚金函数,推出了它所满足的瑕疵离散更新方程,进而得出了它的递推解,显示解和渐近解.In this paper, under the negative binomial（2） risk process, discounted value of a penalty at ruin is examined, which is considered as a function of the initial surplus, and is usually called Gerber-Shui penalty function. It＇s shown to satisfy a defective and discrete renewal equation, and its recursive solution, explicit solution and approximative solution are also derived.

关 键 词：负二项(2)风险过程 破产概率 Gerber—Shui罚金函数 瑕疵离散更新方程 

分 类 号：O211.62[理学—概率论与数理统计] O211.3[理学—数学]