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A Risk Model with an Observer in a Markov Environment

Hansjörg Albrecher () and Jevgenijs Ivanovs ()
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Hansjörg Albrecher: Department of Actuarial Science, University of Lausanne, Lausanne CH-1015, Switzerland
Jevgenijs Ivanovs: Department of Actuarial Science, University of Lausanne, Lausanne CH-1015, Switzerland

Risks, 2013, vol. 1, issue 3, 1-14

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 (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 M2 M4 K2 (search for similar items in EconPapers)
Date: 2013
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