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Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model

Published online by Cambridge University Press:  17 April 2015

Andrew C.Y. Ng  and
Hailiang Yang
Andrew C.Y. Ng
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
Hailiang Yang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
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Abstract

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In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.

Keywords

Markov-modulated risk modeljoint distribution of surplus immediately before and at ruinchange of probability measureexponential martingaleLundberg-type bounds
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 35 , Issue 2 , November 2005 , pp. 351 - 361
Copyright
Copyright © ASTIN Bulletin 2005

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