On orderings and bounds in a generalized Sparre Andersen risk model

被引：6

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：

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY | 2011年 / 27卷 / 01期

关键词：

Gerber-Shiu function; Sparre Andersen risk model; last interclaim time; claim causing ruin; last ladder height; stochastic ordering; NBU; NWU; DISTRIBUTIONS; DEPENDENCE;

D O I：

10.1002/asmb.837

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

A generalization of the Gerber-Shiu function proposed by (Cheung et al., Scand. Actuarial J., in press, 2010) is used to derive some ordering properties for certain ruin-related quantities in a Sparre Andersen type risk model. Additional bounds and/or refinements can be obtained by further assuming that the claim size and the interclaim time distributions possess certain reliability properties. Finally, numerical examples are considered to compare the exact solution to the bounds. Copyright (C) 2010 John Wiley & Sons, Ltd.

引用

页码：51 / 60

页数：10

共 20 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] 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
[3] Barlow R.E., 1981, STAT THEORY RELIABIL
[4] BOUDREAULT M, 2006, SCANDINAVIAN ACTUARI, P265
[5] CHEUNG E. C. K., 2010, SCANDINAVIAN ACTUARI
[6] 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
[7] 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
[8] Denuit M, 2005, ACTUARIAL THEORY FOR DEPENDENT RISKS: MEASURES, ORDERS AND MODELS, P1, DOI 10.1002/0470016450
[9] PRESERVATION OF CERTAIN CLASSES OF LIFE DISTRIBUTIONS UNDER POISSON SHOCK-MODELS
FAGIUOLI, E
PELLEREY, F
[J]. JOURNAL OF APPLIED PROBABILITY, 1994, 31 (02) : 458 - 465
[10] FAGIUOLI E, 1993, NAV RES LOG, V40, P829, DOI 10.1002/1520-6750(199310)40:6<829::AID-NAV3220400607>3.0.CO

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