A Proof of Lehoczky's Theorem on Drawdowns

TL;DR

This paper provides a proof of Lehoczky's drawdown formula for one-dimensional diffusion processes by analyzing the Poisson structure of their excursions below the running maximum.

Contribution

It introduces a novel proof of Lehoczky's theorem utilizing excursion theory and Poisson processes, offering new insights into diffusion process behavior.

Findings

Proof of Lehoczky's drawdown formula established.

Excursion theory applied to diffusion processes below maximum.

Enhanced understanding of drawdown behavior in stochastic processes.

Abstract

We give a proof of Lehoczky's drawdown formula for one-dimensional diffusion processes, using the Poisson structure of the excursions of the diffusion below its running maximum.