TY - JOUR
T1 - A Joint Density Function in Phase-Type (2) Risk Model
AU - Xu , Huai
AU - Tang , Ling
JO - Communications in Mathematical Research 
VL - 4
SP - 349
EP - 358
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19036.html
KW - Gerber-Shiu discounted penalty function, phase-type (2) distribution,
surplus prior to ruin, deficit at ruin.
AB - <p style="text-align: justify;">In this paper, we consider a Gerber-Shiu discounted penalty function in
Sparre 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 differential
equation. By conditioning on the time and the amount of the first claim, we derive
a Laplace transform of the Gerber-Shiu discounted penalty function, and then we
consider the joint density function of the surplus prior to ruin and the deficit at ruin
and some ruin related problems. Finally, we give a numerical example to illustrate
the application of the results.</p>