A Joint Density Function in the Renewal Risk Model

被引：0

作者：

Xu Huai ^{[1
]}

Tang Ling ^{[2
]}

Wang De-hui

机构：

[1] School of Mathematics,Anhui University

[2] Department of mathematics,Anhui Institute of Architecture and Industry

来源：

Communications in Mathematical Research | 2013年 / 29卷 / 01期

关键词：

deficit at ruin; surplus prior to ruin; phase-type distribution; renewal risk model; maximal aggregate loss;

D O I：

10.13447/j.1674-5647.2013.01.001

中图分类号：

O211.3 [分布理论];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper,we consider a general expression for(u,x,y),the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u.In the renewal risk model,this density function is expressed in terms of the corresponding density function when the initial surplus is 0.In the compound Poisson risk process with phase-type claim size,we derive an explicit expression for(u,x,y).Finally,we give a numerical example to illustrate the application of these results.

引用

页码：88 / 96

页数：9

共 7 条

[1] ON THE UPCROSSING AND DOWNCROSSING PROBABILITIES OF A DUAL RISK MODEL WITH PHASE-TYPE GAINS
Ng, Andrew C. Y.
[J]. ASTIN BULLETIN, 2010, 40 (01): : 281 - 306
[2] The Time of Recovery and the Maximum Severity of Ruin in a Sparre Andersen Model,
Wu, Xueyuan
[J]. NORTH AMERICAN ACTUARIAL JOURNAL, 2008, 12 (04) : 425 - 427
[3] On the ruin time distribution for a Sparre Andersen process with exponential claim sizes
Borovkov, Konstantin A.
Dickson, David C. M.
[J]. INSURANCE MATHEMATICS & ECONOMICS, 2008, 42 (03) : 1104 - 1108
[4] On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model *[J] . Hansj?rg Albrecher,Jürgen Hartinger,Stefan Thonhauser.ASTIN Bulletin . 2007 (2)
[5] THE TIME VALUE OF RUIN IN A SPARRE ANDERSEN MODEL
Gerber, Hans
Shiu, Elias
[J]. NORTH AMERICAN ACTUARIAL JOURNAL, 2005, 9 (02) : 49 - 69
[6] The deficit at ruin in the stationary renewal risk model[J] . Gordon Willmot.Scandinavian Actuarial Journal . 2004 (4)
[7] On the Distribution of the Deficit at Ruin when Claims are Phase-type[J] . Steve Drekic,David C. M. Dickson,David A. Stanford,Gordon E. Willmot.Scandinavian Actuarial Journal . 2004 (2)

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