The Outstanding Claims Reserve Based On The GPSJ₁ Process

In non-life insurance actuarial field, the calculation of outstanding claims reserve needed two key variables: loss(or claims) and the number of claims. Loss dates distribution always had heavy tail, such as Weibull distribution and Pareto distribution. There were many theory reasoning and practical proof about heavy tails. For example, Soohan Ahn etc tried to apply new distribution class Log PH(phase-type) class to describe loss. Log PH(phase-type) class included lots of heavy tail distributions as well as some good tail characters so that it could fit dates better. As to claims number, a lot of scholars tried to find the distribution or similar distribution by data fitting, then got further compound distribution or boundary values. In this paper, we used GPSJ1 distribution class, which was used widely, contained a lot of distributions, and had complete related theory. We assumed that the claim number submited to GPSJ1 distribution class, next applied the queuing theory to get the distribution function and its recurrence formula of outstanding claims reserve needed during the certain future period. In this way could we get the evaluation of outstanding loss reserve easier and more practical. Further, we found that the outstanding loss reserve distribution expression included i times convolution F(i)(·). Because of its complication,we recommended IF R class etc to study the bounds of outstanding loss reserve. At the same time, we made a contrastive analysis of these bounds.