On a discrete risk model with two-sided jumps

被引：2

作者：

Yang, Hu ^{[1
]}

Zhang, Zhimin ^{[1
]}

机构：

[1] Chongqing Univ, Dept Stat & Actuarial Sci, Chongqing, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 03期

关键词：

Discrete renewal risk model; Discrete phase-type distribution; Discounted penalty function; Generating function; Recursive formula; EXPECTED DISCOUNTED PENALTY; RUIN; TIME; PROBABILITIES;

D O I：

10.1016/j.cam.2010.01.047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a discrete renewal risk model with phase-type interarrival times and two-sided jumps. In this model, downward jumps represent claim loss, while upward jumps are also allowed to represent random gains. Assume that the downward jumps have an arbitrary probability function and the upward jumps have a rational probability generating function. We study the (Gerber-Shiu) discounted penalty function. The generating function, the recursive formula as well as an explicit expression for the discounted penalty function are obtained. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：835 / 844

页数：10

共 27 条

[1]

[Anonymous], 1999, Introduction to matrix analytic methods in stochastic modeling, DOI DOI 10.1137/1.9780898719734

[2]

Asmussen S., 1996, SCAND ACTUAR J, V1, P19, DOI 10.1080/03461238.1996.10413960

[3]

Asmussen S., 2000, Ruin Probabilities

[4]

Avram F., 2004, ASTIN Bulletin, V34, P315

[5] A review on phase-type distributions and their use in risk theory [J].

Bladt, Mogens .

ASTIN BULLETIN, 2005, 35 (01) :145-161

[6] An ODE approach for the expected discounted penalty at ruin in a jump-diffusion model [J].

Chen, Yu-Ting ;

Lee, Cheng-Few ;

Sheu, Yuan-Chung .

FINANCE AND STOCHASTICS, 2007, 11 (03) :323-355

[7] 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

[8]

Dickson D.C. M., 1994, ASTIN Bulletin, V24, P33, DOI [DOI 10.2143/AST.24.1.2005079, 10.2143/ast.24.1.2005079]

[9]

Gerber H.U., 1988, ASTIN Bull., V18, P161, DOI [10.2143/ast.18.2.2014949, DOI 10.2143/AST.18.2.2014949]

[10] THE TIME VALUE OF RUIN IN A SPARRE ANDERSEN MODEL [J].

Gerber, Hans ;

Shiu, Elias .

NORTH AMERICAN ACTUARIAL JOURNAL, 2005, 9 (02) :49-69

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