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Perturbed MAP Risk Models with Dividend Barrier Strategies

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Eric C. K. Cheung  and
David Landriault
Eric C. K. Cheung*
Affiliation:
University of Waterloo
David Landriault*
Affiliation:
University of Waterloo
*
∗Postal address: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada.
∗Postal address: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada.
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Abstract

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In the context of a dividend barrier strategy (see, e.g. Lin, Willmot and Drekic (2003)) we analyze the moments of the discounted dividend payments and the expected discounted penalty function for surplus processes with claims arriving according to a Markovian arrival process (MAP). We show that a relationship similar to the dividend-penalty identity of Gerber, Lin and Yang (2006) can be established for the class of perturbed MAP surplus processes, extending in the process some results of Li and Lu (2008) for the Markov-modulated risk model. Also, we revisit the same ruin-related quantities in an identical MAP risk model with the only exception that the barrier level effective at time t depends on the state of the underlying environment at this time. Similar relationships are investigated and derived. Numerical examples are also considered.

Keywords

Markovian arrivalperturbed processbarrier strategyGerber–Shiu functiondiscounted dividend payment

MSC classification

Secondary: 60J75: Jump processes 60J25: Continuous-time Markov processes on general state spaces 60J60: Diffusion processes
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 521 - 541
Copyright
Copyright © Applied Probability Trust 2009 

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