A quintuple law for Markov additive processes with phase-type jumps
Lothar Breuer
Source: J. Appl. Probab. Volume 47, Number 2
(2010), 441-458.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1276784902
Digital Object Identifier: doi:10.1239/jap/1276784902
Zentralblatt MATH identifier: 05758480
Mathematical Reviews number (MathSciNet): MR2668499
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