应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2008年
3期
612-621
,共10页
复合更新过程%Erlang(2)分布%积分微分方程%罚金折现期望值函数%破产时刻%二步保费
複閤更新過程%Erlang(2)分佈%積分微分方程%罰金摺現期望值函數%破產時刻%二步保費
복합경신과정%Erlang(2)분포%적분미분방정%벌금절현기망치함수%파산시각%이보보비
Compound renewal process%Erlang(2) distribution%Integro-differential equation%Gerber-Shiu dicounted penalty function%Time of ruin%two-step premium
本文考虑了当索赔间隔时间为Erlang(2)分布且保费收取为二步保费过程的复合更新风险模型,推导出该模型的罚金折现期望值函数满足具有一定边界条件和积分微分方程,并解出该方程.特别地,当索赔额为指数分布时,利用所得结果给出了破产时间的Laplace变换及终积破产概率的解析解.
本文攷慮瞭噹索賠間隔時間為Erlang(2)分佈且保費收取為二步保費過程的複閤更新風險模型,推導齣該模型的罰金摺現期望值函數滿足具有一定邊界條件和積分微分方程,併解齣該方程.特彆地,噹索賠額為指數分佈時,利用所得結果給齣瞭破產時間的Laplace變換及終積破產概率的解析解.
본문고필료당색배간격시간위Erlang(2)분포차보비수취위이보보비과정적복합경신풍험모형,추도출해모형적벌금절현기망치함수만족구유일정변계조건화적분미분방정,병해출해방정.특별지,당색배액위지수분포시,이용소득결과급출료파산시간적Laplace변환급종적파산개솔적해석해.
In this paper,we consider a compound renewal risk process with a two-step premium rate in which the claim waiting times are Erlang(2) distributed.An integro-differential equation with certain boundary condition for Gerber-Shiu function is derived and solved,and use this result we obtain the explicit result about the Laplace transform of the time of ruin and ruin probability when the claim sizes are exponentially distributed.
