A new approach to fluctuations of reflected L\'{e}vy processes

TL;DR

This paper introduces a novel, accessible method for deriving fluctuation identities of reflected Lévy processes with one-sided jumps, avoiding complex theories and enabling broader applicability.

Contribution

The paper presents a new, simplified approach to fluctuation identities for reflected Lévy processes that does not rely on excursion theory or Itô calculus, expanding the scope of results.

Findings

Provides a more general framework for fluctuation identities

Simplifies derivations without using excursion theory or Itô calculus

Achieves broader applicability of fluctuation results

Abstract

We present a new approach to fluctuation identities for reflected L\'{e}vy processes with one-sided jumps. This approach is based on a number of easy to understand observations and does not involve excursion theory or It\^{o} calculus. It also leads to more general results.