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Risks 2013, 1(3), 148-161; doi:10.3390/risks1030148

A Risk Model with an Observer in a Markov Environment

1
Department of Actuarial Science, University of Lausanne, Lausanne CH-1015, Switzerland
2
Swiss Finance Institute, University of Lausanne, Lausanne CH-1015, Switzerland
*
Authors to whom correspondence should be addressed.
Received: 11 October 2013 / Revised: 5 November 2013 / Accepted: 5 November 2013 / Published: 11 November 2013
(This article belongs to the Special Issue Application of Stochastic Processes in Insurance)
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Abstract

We consider a spectrally-negative Markov additive process as a model of a risk process in a random environment. Following recent interest in alternative ruin concepts, we assume that ruin occurs when an independent Poissonian observer sees the process as negative, where the observation rate may depend on the state of the environment. Using an approximation argument and spectral theory, we establish an explicit formula for the resulting survival probabilities in this general setting. We also discuss an efficient evaluation of the involved quantities and provide a numerical illustration. View Full-Text
Keywords: Markov additive process; level-crossing probabilities; Poissonian observation; ruin probability; occupation times Markov additive process; level-crossing probabilities; Poissonian observation; ruin probability; occupation times
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Albrecher, H.; Ivanovs, J. A Risk Model with an Observer in a Markov Environment. Risks 2013, 1, 148-161.

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