Gerber-Shiu analysis with a generalized penalty function

被引：13

作者：

Cheung, Eric C. K. ^{[1
]}

Landriault, David ^{[1
]}

Willmot, Gordon E. ^{[1
]}

Woo, Jae-Kyung ^{[1
]}

机构：

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

来源：

SCANDINAVIAN ACTUARIAL JOURNAL | 2010年 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Defective renewal equation; Dickson-Hipp transform; Compound geometric distribution; Exponential distribution; Mixed Erlang distribution; Phase-type distribution; NBU; NWU; DFR; RUIN;

D O I：

10.1080/03461230902884013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A generalization of the usual penalty function is proposed, and a defective renewal equation is derived for the Gerber-Shiu discounted penalty function in the classical risk model. This is used to derive the trivariate distribution of the deficit at ruin, the surplus prior to ruin, and the surplus immediately following the second last claim before ruin. The marginal distribution of the last interclaim time before ruin is derived and studied, and its joint distribution with the claim causing ruin is derived.

引用

页码：185 / 199

页数：15

共 18 条

[1] Exponential behavior in the presence of dependence in risk theory [J].

Albrecher, H ;

Teugels, JL .

JOURNAL OF APPLIED PROBABILITY, 2006, 43 (01) :257-273

[2]

[Anonymous], 1994, Stochastic models: an algorithmic approach

[3]

Asmussen S., 2000, Ruin Probabilities

[4]

BADESCU AL, 2009, J APPL PROB IN PRESS

[5]

Barlow R.E., 1981, STAT THEORY RELIABIL

[6]

CHEUNG ECK, 2009, STRUCTURAL PRO UNPUB

[7] ON THE DISTRIBUTION OF THE SURPLUS PRIOR TO RUIN [J].

DICKSON, DCM .

INSURANCE MATHEMATICS & ECONOMICS, 1992, 11 (03) :191-207

[8] On the time to ruin for Erlang(2) risk processes [J].

Dickson, DCM ;

Hipp, C .

INSURANCE MATHEMATICS & ECONOMICS, 2001, 29 (03) :333-344

[9] Fitting combinations of exponentials to probability distributions [J].

Dufresne, Daniel .

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, 2007, 23 (01) :23-48

[10] 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

← 1 2 →