A Joint Density Function in Phase-Type (2) Risk Model (Communications in Mathematical Research, 2021)
In this paper, we consider a Gerber-Shiu discounted penalty function inSparre Andersen risk process in which claim inter-arrival times have a phase-type (2)distribution, a distribution with a density satisfying a second order linear differentialequation. By conditioning on the time and the amount of the first claim, we derivea Laplace transform of the Gerber-Shiu discounted penalty function, and then weconsider the joint density function of the surplus prior to ruin and the deficit at ruinand some ruin related problems. Finally, we give a numerical example to illustratethe application of the results.
Keywords: Gerber-Shiu discounted penalty function; phase-type (2) distribution; surplus prior to ruin; deficit at ruin.