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A Markov Additive Risk Process with a Dividend Barrier

Part of: Markov processes Applications Stochastic processes

Published online by Cambridge University Press:  22 February 2016

Esther Frostig
Esther Frostig*
Affiliation:
University of Haifa
*
∗ Postal address: Department of Statistics, University of Haifa, Haifa 31905, Israel. Email address: frostig@stat.haifa.ac.il
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Abstract

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We study a risk process with dividend barrier b where the claims arrive according to a Markovian additive process (MAP). For spectrally negative MAPs, we present linear equations for the expected discounted dividends and the expected discounted penalty function. We apply results for the first exit times of spectrally negative Lévy processes and change-of-measure techniques. Explicit expressions are given when there are positive and negative claims, with phase-type distribution.

Keywords

Markov arrival processspectrally negative Lévy processphase-type distributionexit timereflected process

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics 60G51: Processes with independent increments; L'evy processes 60J27: Continuous-time Markov processes on discrete state spaces 60J75: Jump processes
Secondary: 60G46: Martingales and classical analysis 60J55: Local time and additive functionals
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 2 , June 2013 , pp. 451 - 489
Copyright
© Applied Probability Trust 

Footnotes

Research supported by the Israel Science Foundation, under grant 606/09.

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