On exit times of Levy-driven Ornstein--Uhlenbeck processes

TL;DR

This paper derives explicit formulas for the Laplace transform of exit times in Levy-driven Ornstein--Uhlenbeck processes, using martingale identities, under the assumption of exponentially distributed positive jumps.

Contribution

It introduces two martingale identities that facilitate explicit calculation of exit time Laplace transforms for Levy-driven Ornstein--Uhlenbeck processes.

Findings

Explicit Laplace transform formula for exit times

Martingale identities involving exit times

Application to processes with exponential positive jumps

Abstract

We prove two martingale identities which involve exit times of Levy-driven Ornstein--Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time under the assumption that positive jumps of the Levy process are exponentially distributed.