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Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains

Published online by Cambridge University Press:  28 May 2015

Phung Duy Quang
Phung Duy Quang*
Affiliation:
Department of Mathematics, Foreign Trade University, Hanoi, Vietnam
*
Corresponding author. Email address: [email protected]
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Abstract

This article explores recursive and integral equations for ruin probabilities of generalised risk processes, under rates of interest with homogenous Markov chain claims and homogenous Markov chain premiums. We assume that claim and premium take a countable number of non-negative values. Generalised Lundberg inequalities for the ruin probabilities of these processes are derived via a recursive technique. Recursive equations for finite time ruin probabilities and an integral equation for the ultimate ruin probability are presented, from which corresponding probability inequalities and upper bounds are obtained. An illustrative numerical example is discussed.

Keywords

62P0560G4012E05Integral equationrecursive equationruin probabilityhomogeneous Markov chain
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 3 , August 2014 , pp. 283 - 300
Copyright
Copyright © Global-Science Press 2014

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