Multivariate distribution defined with Farlie-Gumbel-Morgenstern copula and mixed Erlang marginals: Aggregation and capital allocation

被引：48

作者：

Cossette, Helene ^{[1
]}

Cote, Marie-Pier ^{[1
]}

Marceau, Etienne ^{[1
]}

Moutanabbir, Khouzeima ^{[1
]}

机构：

[1] Univ Laval, Ecole Actuariat, Quebec City, PQ, Canada

来源：

INSURANCE MATHEMATICS & ECONOMICS | 2013年 / 52卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Aggregate claim loss; Risk measures; Capital allocation; Tail-Value-at-Risk; FGM copula; TVaR-based allocation rule; Covariance-based allocation rule; Mixed Erlang distribution; RISK MODEL; DEPENDENCE;

D O I：

10.1016/j.insmatheco.2013.03.006

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

In this paper, we investigate risk aggregation and capital allocation problems for a portfolio of possibly dependent risks whose multivariate distribution is defined with the Farlie-Gumbel-Morgenstern copula and mixed Erlang distribution marginals. In such a context, we first show that the aggregate claim amount has a mixed Erlang distribution. Based on a top-down approach, closed-form expressions for the contribution of each risk are derived using the TVaR and covariance rules. These findings are illustrated with numerical examples. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：560 / 572

页数：13

共 32 条

[1] On the coherence of expected shortfall [J].

Acerbi, C ;

Tasche, D .

JOURNAL OF BANKING & FINANCE, 2002, 26 (07) :1487-1503

[2]

Acerbi C., 2001, EXPECTED SHORTFALL T

[3]

[Anonymous], 2005, PRINCETON SERIES FIN

[4]

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

[5]

[Anonymous], 1959, ANN LISUP

[6]

Armstrong M., 2002, WORKING PAPER

[7] Coherent measures of risk [J].

Artzner, P ;

Delbaen, F ;

Eber, JM ;

Heath, D .

MATHEMATICAL FINANCE, 1999, 9 (03) :203-228

[8]

Artzner P., 1999, N AM ACTUARIAL J, V3, P83

[9] TVaR-based capital allocation with copulas [J].

Barges, Mathieu ;

Cossette, Helene ;

Marceau, Etienne .

INSURANCE MATHEMATICS & ECONOMICS, 2009, 45 (03) :348-361

[10] Coherent risk measures, coherent capital allocations and the gradient allocation principle [J].

Buch, A. ;

Dorfleitner, G. .

INSURANCE MATHEMATICS & ECONOMICS, 2008, 42 (01) :235-242

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