Occupation times in the MAP risk model

David Landriault and Tianxiang Shi

Insurance: Mathematics and Economics, 2015, vol. 60, issue C, 75-82

Abstract: Occupation times have so far been primarily analyzed in the class of Lévy processes, most notably some of its special cases, by capitalizing on the stationary and independence property of the process increments. In this paper, we relax this assumption and provide a closed-form expression for the Laplace transform of occupation times for surplus processes governed by a Markovian claim arrival process. This will naturally allow us to revisit some occupation time results for the compound Poisson risk model. We also identify the density of the total duration of negative surplus and its individual contributions when the number of claims occurring with negative surplus levels is jointly studied. Finally, a numerical example in an Erlang-2 renewal risk process is also considered.

Keywords: Occupation time; Duration of negative surplus; Markovian arrival process; Time to ruin; Number of claims with negative surplus (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:60:y:2015:i:c:p:75-82

DOI: 10.1016/j.insmatheco.2014.10.014

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