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Conditional tail expectations for multivariate phase-type distributions

Part of: Mathematical economics Applications Distribution theory

Published online by Cambridge University Press:  14 July 2016

Jun Cai  and
Haijun Li
Jun Cai*
Affiliation:
University of Waterloo
Haijun Li*
Affiliation:
Washington State University
*
∗Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada. Email address: jcai@math.uwaterloo.ca
∗∗Postal address: Department of Mathematics, Washington State University, Pullman, WA 99164, USA. Email address: lih@math.wsu.edu
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Abstract

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The conditional tail expectation in risk analysis describes the expected amount of risk that can be experienced given that a potential risk exceeds a threshold value, and provides an important measure of right-tail risk. In this paper, we study the convolution and extreme values of dependent risks that follow a multivariate phase-type distribution, and derive explicit formulae for several conditional tail expectations of the convolution and extreme values for such dependent risks. Utilizing the underlying Markovian property of these distributions, our method not only provides structural insight, but also yields some new distributional properties of multivariate phase-type distributions.

Keywords

Univariate phase-type distributionmultivariate phase-type distributioncontinuous-time Markov chainconvolutionextreme valueMarshall-Olkin distributionconditional tail expectationexcess lossresidual lifetime

MSC classification

Primary: 62E15: Exact distribution theory
Secondary: 62P05: Applications to actuarial sciences and financial mathematics 91B30: Risk theory, insurance
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 810 - 825
Copyright
© Applied Probability Trust 2005 

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