Tail Moments of Compound Distributions

18 Pages Posted: 14 Jul 2021

See all articles by Jiandong Ren

Jiandong Ren

University of Western Ontario

Date Written: July 5, 2021


In this paper, we study the moment transform of both univariate and multivariate compound sums. We first derive simple explicit formulas for the first and second moment transforms when the (loss) frequency distribution is in the so-called (a,b,0) class. Then we show that the derived formulas can be used to efficiently compute risk measures such as the Tail Conditional Expectation (TCE), the Tail Variance (TV) and higher tail moments. The results generalize those in Denuit (2020).

Keywords: Compound distribution, dependence modeling, size-biased transform, risk measures, capital allocation, weighted distributions

JEL Classification: C10, C60

Suggested Citation

Ren, Jiandong, Tail Moments of Compound Distributions (July 5, 2021). Available at SSRN: https://ssrn.com/abstract=3880127 or http://dx.doi.org/10.2139/ssrn.3880127

Jiandong Ren (Contact Author)

University of Western Ontario ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8

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