Year: 2013
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 88–96
Abstract
In this paper, we consider a general expression for $ϕ(u, x, y)$, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is $u$. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is 0. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for $ϕ(u, x, y)$. Finally, we give a numerical example to illustrate the application of these results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-CMR-19031
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 88–96
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: deficit at ruin surplus prior to ruin phase-type distribution renewal risk model maximal aggregate loss.