A quintuple law for Markov--additive processes with phase--type jumps

Breuer, Lothar (2010) A quintuple law for Markov--additive processes with phase--type jumps. Journal of Applied Probability, 47 (2). pp. 441-458. ISSN 0021-9002. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1239/jap/1276784902

Abstract

We consider a Markov additive process (MAP) with phase-type jumps, starting at 0. Given a positive level u, we determine the joint distribution of the undershoot and overshoot of the first jump over the level u, the maximal level before this jump, the time of attaining this maximum, and the time between the maximum and the jump. The analysis is based on first passage times and time reversion of MAPs. A marginal of the derived distribution is the Gerber-Shiu function, which is of interest to insurance risk. Several examples serve to compare the present result with the literature.

Item Type: Article
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: Lothar Breuer
Date Deposited: 29 Jun 2011 13:35
Last Modified: 08 Feb 2012 12:32
Resource URI: http://kar.kent.ac.uk/id/eprint/23880 (The current URI for this page, for reference purposes)
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