On the exit from a finite interval for the risk processes with stochastic premiums

Abstract

In this article the almost semi-continuous step-process $\xi (t)$ is considered. The conditional characteristic functions of the jumps of $\xi (t)$ have the form $\mathrm{E}[e^{i\alpha {\xi }_k}/{\xi }_k>0]=c(c-i\alpha {)}^{-1}$. For such processes the boundary functionals connected with the exit from the finite interval are investigated.

11 pages