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On the Upcrossing and Downcrossing Probabilities of a Dual Risk Model With Phase-Type Gains

Published online by Cambridge University Press:  09 August 2013

Andrew C.Y. Ng
Andrew C.Y. Ng*
Affiliation:
Department of Finance, The Chinese University of Hong Kong, Shatin, Hong Kong
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Abstract

In this paper, we consider the dual of the classical Cramér-Lundberg model when gains follow a phase-type distribution. By using the property of phase-type distribution, two pairs of upcrossing and downcrossing barrier probabilities are derived. Explicit formulas for the expected total discounted dividends until ruin and the Laplace transform of the time of ruin under a variety of dividend strategies can then be obtained without the use of Laplace transforms.

Keywords

Ruin theorydual risk modelphase-type distributiondividend strategyupcrossing and downcrossing probabilities
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 281 - 306
Copyright
Copyright © International Actuarial Association 2010

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