A Proof of Lehoczky's Theorem on Drawdowns

P.J. Fitzsimmons

A Proof of Lehoczky's Theorem on Drawdowns

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arxiv 2209.04695 v1 pith:SI2ONHR4 submitted 2022-09-10 math.PR

P.J. Fitzsimmons This is my paper · ORCID

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keywords diffusionlehoczkyproofbelowdrawdowndrawdownsexcursionsformula

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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.

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Drawdowns of diffusions
math.PR 2024-11 conditional novelty 6.0 of 10

The authors prove Lehoczky's and Malyutin's drawdown formulas via excursion theory and analyze the Markov process of the maximum at the first drawdown time.

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