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.
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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.
|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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