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Occupation times in the MAP risk model

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  • Landriault, David
  • Shi, Tianxiang

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.

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  • Landriault, David & Shi, Tianxiang, 2015. "Occupation times in the MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 75-82.
    • Handle: RePEc:eee:insuma:v:60:y:2015:i:c:p:75-82
    DOI: 10.1016/j.insmatheco.2014.10.014
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    2. Yingchun Deng & Xuan Huang & Ya Huang & Xuyan Xiang & Jieming Zhou, 2020. "n-Dimensional Laplace Transforms of Occupation Times for Pre-Exit Diffusion Processes," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 345-360, March.

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