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

TL;DR

This paper investigates boundary functionals related to the exit times of a semi-continuous step-process with specific jump characteristics, contributing to the understanding of risk processes with stochastic premiums.

Contribution

It introduces a new analysis of boundary functionals for a semi-continuous process with particular jump distributions in the context of risk processes.

Findings

Derived explicit formulas for boundary functionals

Analyzed exit times for processes with specific jump distributions

Extended risk process theory to semi-continuous step-processes

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.