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A Risk Model with an Observer in a Markov Environment
Department of Actuarial Science, University of Lausanne, Lausanne CH-1015, Switzerland
Swiss Finance Institute, University of Lausanne, Lausanne CH-1015, Switzerland
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Received: 11 October 2013; in revised form: 5 November 2013 / Accepted: 5 November 2013 / Published: 11 November 2013
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.
Albrecher H, Ivanovs J. A Risk Model with an Observer in a Markov Environment. Risks. 2013; 1(3):148-161.
Albrecher, Hansjörg; Ivanovs, Jevgenijs. 2013. "A Risk Model with an Observer in a Markov Environment." Risks 1, no. 3: 148-161.