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A generalization of multivariate Pareto distributions: tail risk measures, divided differences and asymptotics

Content Provider	Scilit
Author	Hendriks, Harrie Landsman, Zinoviy
Copyright Year	2016
Description	Journal: Scandinavian Actuarial Journal We consider a multivariate distribution of the form , where the survival function h is a multiply monotonic function of order such that , for all i and for . This generalizes work by Chiragiev and Landsman on completely monotonic survival functions. We show that the considered dependence structure is more flexible in the sense that the correlation coefficient between two components may attain negative values. We demonstrate that the tool of divided difference is very convenient for evaluation of tail risk measures and their allocations. In terms of divided differences, formulas for tail conditional expectation (tce), tail conditional variance and tce-based capital allocation are obtained. We obtain a closed form for the capital allocation of aggregate risk. Special attention is paid to survival functions h that are regularly or rapidly varying.
Related Links	https://www.tandfonline.com/doi/pdf/10.1080/03461238.2016.1255249?needAccess=true
Ending Page	803
Page Count	19
Starting Page	785
ISSN	03461238
e-ISSN	16512030
DOI	10.1080/03461238.2016.1255249
Journal	Scandinavian Actuarial Journal
Issue Number	9
Volume Number	2017
Language	English
Publisher	Informa UK Limited
Publisher Date	2016-11-09
Access Restriction	Open
Subject Keyword	Journal: Scandinavian Actuarial Journal Statistics and Probability Exponential Distribution Pareto Distribution Divided Differences Tail Conditional Expectation Tail Conditional Correlation Regular Variation Rapid Variation
Content Type	Text
Subject	Statistics and Probability Economics and Econometrics Statistics, Probability and Uncertainty

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