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.
A Proof of Lehoczky's Theorem on Drawdowns
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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.
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Drawdowns of diffusions
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.