Gerber-Shiu analysis in a perturbed risk model with dependence between claim sizes and interclaim times

被引：29

作者：

Zhang, Zhimin ^{[1
]}

Yang, Hu ^{[1
]}

机构：

[1] Chongqing Univ, Dept Stat & Actuarial Sci, Chongqing 630044, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2011年 / 235卷 / 05期

关键词：

Gerber-Shiu function; Dependence; Integro-differential equation; Laplace transform; Ruin probability; DEFECTIVE RENEWAL EQUATION; RUIN;

D O I：

10.1016/j.cam.2010.08.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider a compound Poisson risk model perturbed by a Brownian motion. We construct the bivariate cumulative distribution function of the claim size and interclaim time by Farlie-Gumbel-Morgenstern copula. The integro-differential equations and the Laplace transforms for the Gerber-Shiu functions are obtained. We also show that the Gerber-Shiu functions satisfy some defective renewal equations. For exponential claims, some explicit expressions are obtained, and numerical examples for the ruin probabilities are also given. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1189 / 1204

页数：16

共 50 条

[31] Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims
Wei, Li
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2012, 28 (01): : 31 - 38
[32] Estimating the Gerber-Shiu Expected Discounted Penalty Function for Levy Risk Model
Huang, Yujuan
Yu, Wenguang
Pan, Yu
Cui, Chaoran
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2019, 2019
[33] A REINSURANCE RISK MODEL WITH A THRESHOLD COVERAGE POLICY: THE GERBER-SHIU PENALTY FUNCTION
Boxma, O. J.
Frostig, E.
Perry, D.
JOURNAL OF APPLIED PROBABILITY, 2017, 54 (01) : 267 - 285
[34] Asymptotic Estimates of Gerber-Shiu Functions in the Renewal Risk Model with Exponential Claims
Li WEI1
Acta Mathematicae Applicatae Sinica, 2012, (01) : 31 - 38
[35] The Gerber-Shiu discounted penalty functions for a risk model with two classes of claims
Zhang, Zhimin
Li, Shuanming
Yang, Hu
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 230 (02) : 643 - 655
[36] The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function
Pavlova, KP
Willmot, GE
INSURANCE MATHEMATICS & ECONOMICS, 2004, 35 (02): : 267 - 277
[37] Gerber-Shiu function of a discrete risk model with and without a constant dividend barrier
Shanshan Wang
Chuangji An
Chunsheng Zhang
Frontiers of Mathematics in China, 2015, 10 : 377 - 393
[38] Estimating the Gerber-Shiu function in a Levy risk model by Laguerre series expansion
Zhang, Zhimin
Su, Wen
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 346 : 133 - 149
[39] On a risk model with dependence between claim sizes and claim intervals
Meng, Qingbin
Zhang, Xin
Guo, Junyi
STATISTICS & PROBABILITY LETTERS, 2008, 78 (13) : 1727 - 1734
[40] The Markovian Shot-noise Risk Model: A Numerical Method for Gerber-Shiu Functions
Pojer, Simon
Thonhauser, Stefan
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2023, 25 (01)

← 1 2 3 4 5 →