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

Lothar Breuer
2010 Journal of Applied Probability  
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
more » ... of interest to insurance risk. Several examples serve to compare the present result with the literature.
doi:10.1239/jap/1276784902 fatcat:x3fdkbkmzze23dllyjwqb6embe