A note on deficit analysis in dependency models involving Coxian claim amounts

被引：6

作者：

Landriault, David ^{[1
]}

Lee, Wing Yan ^{[1
]}

Willmot, Gordon E. ^{[1
]}

Woo, Jae-Kyung ^{[2
]}

机构：

[1] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada

[2] Univ Hong Kong, Dept Stat & Actuarial Sci, Pokfulam, Hong Kong, Peoples R China

来源：

SCANDINAVIAN ACTUARIAL JOURNAL | 2014年 / 2014卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

dependent Sparre Andersen risk model; Coxian-type claim sizes; time to ruin; deficit at ruin; Lundberg's generalized equation; Lagrange polynomials; Vandemonde matrix; Cauchy matrix; DISCOUNTED PENALTY-FUNCTION; RISK MODEL; RUIN; SURPLUS; TIME;

D O I：

10.1080/03461238.2012.723044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a fairly large class of dependent Sparre Andersen risk models where the claim sizes belong to the class of Coxian distributions. We analyze the Gerber-Shiu discounted penalty function when the penalty function depends on the deficit at ruin. We show that the system of equations needed to solve for this quantity is surprisingly simple. Various applications of this result are also considered.

引用

页码：405 / 423

页数：19

共 23 条

[1] Exponential behavior in the presence of dependence in risk theory
Albrecher, H
Teugels, JL
[J]. JOURNAL OF APPLIED PROBABILITY, 2006, 43 (01) : 257 - 273
[2] Albrecher H, 2010, N AM ACTUAR J, V14, P420, DOI 10.1080/10920277.2010.10597599
[3] [Anonymous], 1997, ART COMPUTER PROGRAM
[4] [Anonymous], 2006, An introduction to copulas
[5] DEPENDENT RISK MODELS WITH BIVARIATE PHASE-TYPE DISTRIBUTIONS
Badescu, Andrei L.
Cheung, Eric C. K.
Landriault, David
[J]. JOURNAL OF APPLIED PROBABILITY, 2009, 46 (01) : 113 - 131
[6] Boudreault M., 2006, SCAND ACTUAR J, V5, P265
[7] Chadjiconstantinidis S., 2013, SCANDINAVIA IN PRESS
[8] A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium
Cheung, Eric C. K.
[J]. INSURANCE MATHEMATICS & ECONOMICS, 2011, 48 (03) : 384 - 397
[9] Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models
Cheung, Eric C. K.
Landriault, David
Willmot, Gordon E.
Woo, Jae-Kyung
[J]. INSURANCE MATHEMATICS & ECONOMICS, 2010, 46 (01) : 117 - 126
[10] On the compound Poisson risk model with dependence based on a generalized Farlie-Gumbel-Morgenstern copula
Cossette, Helene
Marceau, Etienne
Marri, Fouad
[J]. INSURANCE MATHEMATICS & ECONOMICS, 2008, 43 (03) : 444 - 455

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