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Tail Conditional Expectations for Exponential Dispersion Models

Published online by Cambridge University Press:  17 April 2015

Zinoviy Landsman  and
Emiliano A. Valdez
Zinoviy Landsman
Affiliation:
Actuarial Research Center, Department of Statistics – University of Haifa, Mount Carmel, Haifa 31905, Israel, E-mail: landsman@stat.haifa.ac.il
Emiliano A. Valdez
Affiliation:
School of Actuarial Studies, Faculty of Commerce & Economics – University of New South Wales, Sydney, Australia 2052, E-mail: e.valdez@unsw.edu.au
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Abstract

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There is a growing interest in the use of the tail conditional expectation as a measure of risk. For an institution faced with a random loss, the tail conditional expectation represents the conditional average amount of loss that can be incurred in a fixed period, given that the loss exceeds a specified value. This value is typically based on the quantile of the loss distribution, the so-called value-at-risk. The tail conditional expectation can therefore provide a measure of the amount of capital needed due to exposure to loss. This paper examines this risk measure for “exponential dispersion models”, a wide and popular class of distributions to actuaries which, on one hand, generalizes the Normal and shares some of its many important properties, but on the other hand, contains many distributions of nonnegative random variables like the Gamma and the Inverse Gaussian.

Keywords

Tail value-at-riskTail conditional expectationsExponential dispersion family
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 1 , May 2005 , pp. 189 - 209
Copyright
Copyright © ASTIN Bulletin 2005

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