Survival probabilities in a discrete semi-Markov risk model

被引:12
作者
Chen, Mi [1 ]
Yuen, Kam Chuen [2 ]
Guo, Junyi [3 ]
机构
[1] Fujian Normal Univ, Sch Math & Comp Sci, Fuzhou 350108, Peoples R China
[2] Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China
[3] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
基金
中国国家自然科学基金;
关键词
Generating function; Recursive formula; Semi-Markov risk model; Survival probability; RUIN PROBABILITIES; PENALTY-FUNCTION;
D O I
10.1016/j.amc.2014.01.057
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider the survival probability for a discrete semi-Markov risk model, which assumes individual claims are influenced by a Markov chain with finite state space and there is autocorrelation among consecutive claim sizes. Our semi-Markov risk model is similar to the one studied in Reinhard and Snoussi (2001,2002) [1,2] without the restriction imposed on the distributions of the claims. In particular, the model of study includes several existing risk models such as the compound binomial model (with time-correlated claims) and the compound Markov binomial model (with time-correlated claims) as special cases. The main purpose of the paper is to develop a recursive method for computing the survival probability in the two-state model, and present some numerical examples to illustrate the application of our results. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:205 / 215
页数:11
相关论文
共 26 条
[1]   On the discounted penalty function in a Markov-dependent risk model [J].
Albrecher, H ;
Boxma, OJ .
INSURANCE MATHEMATICS & ECONOMICS, 2005, 37 (03) :650-672
[2]  
Chen M., 2013, EXPECTED DISCO UNPUB
[3]   Discounted probabilities and ruin theory in the compound binomial model [J].
Cheng, SX ;
Gerber, HU ;
Shiu, ESW .
INSURANCE MATHEMATICS & ECONOMICS, 2000, 26 (2-3) :239-250
[4]   ANALYSIS OF A GENERALIZED PENALTY FUNCTION IN A SEMI-MARKOVIAN RISK MODEL [J].
Cheung, Eric ;
Landriault, David .
NORTH AMERICAN ACTUARIAL JOURNAL, 2009, 13 (04) :497-513
[5]   Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model [J].
Cossette, H ;
Landriault, D ;
Marceau, T .
INSURANCE MATHEMATICS & ECONOMICS, 2004, 34 (03) :449-466
[6]  
Cossette H., 2003, SCAND ACTUAR J, V2003, P301
[7]  
Dickson D.C. M., 1994, ASTIN Bulletin, V24, P33, DOI [DOI 10.2143/AST.24.1.2005079, 10.2143/ast.24.1.2005079]
[8]   A numerical method for the expected penalty-reward function in a Markov-modulated jump-diffusion process [J].
Diko, Peter ;
Usabel, Miguel .
INSURANCE MATHEMATICS & ECONOMICS, 2011, 49 (01) :126-131
[9]  
Gerber H.U., 1988, ASTIN Bull., V18, P161, DOI [10.2143/ast.18.2.2014949, DOI 10.2143/AST.18.2.2014949]
[10]   An elementary approach to discrete models of dividend strategies [J].
Gerber, Hans U. ;
Shiu, Elias S. W. ;
Yang, Hailiang .
INSURANCE MATHEMATICS & ECONOMICS, 2010, 46 (01) :109-116