On the Expected Discounted Penalty Function in a Delayed-claims Risk Model

被引:6
作者
Meng, Hui [1 ]
Wang, Guo-jing [2 ,3 ]
机构
[1] Cent Univ Finance & Econ, China Inst Actuarial Sci, Beijing 100081, Peoples R China
[2] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China
[3] Soochow Univ, Ctr Financial Engn, Suzhou 215006, Peoples R China
来源
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES | 2012年 / 28卷 / 02期
关键词
main claim; by-claim; penalty function; generalized Lundberg's equation; operator; renewal equation; RUIN; TIME;
D O I
10.1007/s10255-012-0141-y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounted penalty function, and derive the defective renewal equation satisfied by it. We obtain some explicit results when the main claim and the by-claim are both exponentially distributed, respectively. We also present some numerical illustrations.
引用
收藏
页码:215 / 224
页数:10
相关论文
共 10 条
[1]   A ruin model with dependence between claim sizes and claim intervals [J].
Albrecher, H ;
Boxma, OJ .
INSURANCE MATHEMATICS & ECONOMICS, 2004, 35 (02) :245-254
[2]  
Boudreault M., 2006, Scandinavian Actuarial Journal, V5, P265
[3]   On the time to ruin for Erlang(2) risk processes [J].
Dickson, DCM ;
Hipp, C .
INSURANCE MATHEMATICS & ECONOMICS, 2001, 29 (03) :333-344
[4]   THE SURPLUSES IMMEDIATELY BEFORE AND AT RUIN, AND THE AMOUNT OF THE CLAIM CAUSING RUIN [J].
DUFRESNE, F ;
GERBER, HU .
INSURANCE MATHEMATICS & ECONOMICS, 1988, 7 (03) :193-199
[5]   The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin [J].
Gerber, HU ;
Shiu, ESW .
INSURANCE MATHEMATICS & ECONOMICS, 1997, 21 (02) :129-137
[6]  
Gerber HU., 1998, North Amer-ican Actuarial Journal, V2, P48, DOI [10.1080/10920277.1998.10595671, DOI 10.1080/10920277.1998.10595671]
[7]   On ruin for the Erlang(n) risk process [J].
Li, SM ;
Garrido, J .
INSURANCE MATHEMATICS & ECONOMICS, 2004, 34 (03) :391-408
[8]   Joint distributions of some actuarial random vectors containing the time of ruin [J].
Wu, R ;
Wang, GJ ;
Wei, L .
INSURANCE MATHEMATICS & ECONOMICS, 2003, 33 (01) :147-161
[9]   Ultimate ruin in a delayed-claims risk model [J].
Yuen, KC ;
Guo, JY ;
Ng, KW .
JOURNAL OF APPLIED PROBABILITY, 2005, 42 (01) :163-174
[10]   Ruin probabilities for time-correlated claims in the compound binomial model [J].
Yuen, KC ;
Guo, JY .
INSURANCE MATHEMATICS & ECONOMICS, 2001, 29 (01) :47-57