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Ruin problems in Markov-modulated risk models

Published online by Cambridge University Press:  30 May 2017

David C.M. Dickson  and
Marjan Qazvini
David C.M. Dickson*
Affiliation:
Department of Economics, Centre for Actuarial Studies, University of Melbourne, Melbourne, VIC 3010, Australia
Marjan Qazvini
Affiliation:
Department of Economics, Centre for Actuarial Studies, University of Melbourne, Melbourne, VIC 3010, Australia
*
*Correspondence to: David C.M. Dickson, Department of Economics, Centre for Actuarial Studies, The University of Melbourne, Melbourne, VIC 3010, Australia. Tel: +61 3 8344 4727. Fax: +61 3 8344 6899. E-mail: dcmd@unimelb.edu.au
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Abstract

Chen et al. (2014), studied a discrete semi-Markov risk model that covers existing risk models such as the compound binomial model and the compound Markov binomial model. We consider their model and build numerical algorithms that provide approximations to the probability of ultimate ruin and the probability and severity of ruin in a continuous time two-state Markov-modulated risk model. We then study the finite time ruin probability for a discrete m-state model and show how we can approximate the density of the time of ruin in a continuous time Markov-modulated model with more than two states.

Keywords

Discrete time modelMarkov-modulated modelFinite time ruin probabilitySeverity of ruin
Type
Papers
Information
Annals of Actuarial Science , Volume 12 , Issue 1 , March 2018 , pp. 23 - 48
Copyright
© Institute and Faculty of Actuaries 2017 

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