TY - JOUR
T1 - A multivariate dependence measure for aggregating risks
AU - Dhaene, Jan
AU - Linders, Daniël
AU - Schoutens, Wim
AU - Vyncke, David
N1 - Funding Information:
Jan Dhaene, Daniël Linders and Wim Schoutens acknowledge the financial support of the Onderzoeksfonds K.U. Leuven (GOA/12/002/TBA: Management of Financial and Actuarial Risks: Modeling, Regulation, Incentives and Market Effects). Further, the authors would like to thank the referees for their valuable comments.
PY - 2014/6
Y1 - 2014/6
N2 - To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other hand, assuming a comonotonic dependence structure will likely overrate the real aggregate risk. In order to choose between the two approximations, or perhaps use a weighted average, we should have an indication of the accuracy. Clearly this accuracy will depend on the copula between the individual risk factors, but it is also influenced by the marginal distributions. In this paper we introduce a multivariate dependence measure that takes both aspects into account. This new measure differs from other multivariate dependence measures, as it focuses on the aggregate risk rather than on the copula or the joint distribution function itself. We prove several interesting properties of this new measure and discuss its relation to other dependence measures. We also give some comments on the estimation and conclude with examples and numerical results.
AB - To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other hand, assuming a comonotonic dependence structure will likely overrate the real aggregate risk. In order to choose between the two approximations, or perhaps use a weighted average, we should have an indication of the accuracy. Clearly this accuracy will depend on the copula between the individual risk factors, but it is also influenced by the marginal distributions. In this paper we introduce a multivariate dependence measure that takes both aspects into account. This new measure differs from other multivariate dependence measures, as it focuses on the aggregate risk rather than on the copula or the joint distribution function itself. We prove several interesting properties of this new measure and discuss its relation to other dependence measures. We also give some comments on the estimation and conclude with examples and numerical results.
KW - Aggregate distribution
KW - Comonotonic copula
KW - Concordance order
KW - Independence
KW - Positive quadrant dependence
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U2 - 10.1016/j.cam.2013.12.010
DO - 10.1016/j.cam.2013.12.010
M3 - Article
AN - SCOPUS:84891438063
SN - 0377-0427
VL - 263
SP - 78
EP - 87
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -