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

A Risk Model with an Observer in a Markov Environment

Received: 11 October 2013; in revised form: 5 November 2013 / Accepted: 5 November 2013 / Published: 11 November 2013
(This article belongs to the Special Issue Application of Stochastic Processes in Insurance)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Keywords: Markov additive process; level-crossing probabilities; Poissonian observation; ruin probability; occupation times
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MDPI and ACS Style

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

AMA Style

Albrecher H, Ivanovs J. A Risk Model with an Observer in a Markov Environment. Risks. 2013; 1(3):148-161.

Chicago/Turabian Style

Albrecher, Hansjörg; Ivanovs, Jevgenijs. 2013. "A Risk Model with an Observer in a Markov Environment." Risks 1, no. 3: 148-161.

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