The Local Time of the Classical Risk Process

Abstract

In this paper we give an explicit expression for the local time of the classical risk process and associate it with the density of an occupational measure. To do so, we approximate the local time by a suitable sequence of absolutely continuous random fields. Also, as an application, we analyze the mean of the times $s\in [0,T]$ such that $0\le X_s\le X_{s+\epsilon }$ for some given $\epsilon >0$.

15 pages