On Azéma-Yor processes, their optimal properties and the Bachelier-drawdown equation
On Azéma-Yor processes, their optimal properties and the Bachelier-drawdown equation
We study the class of Az\'ema-Yor processes defined from a general semimartingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. Solutions of the latter have the drawdown property: …