Summary: On the Maximum Drawdown of a Brownian Motion
Malik Magdon-Ismail Amir F. Atiya
Department of Computer Science, Department of Computer Engineering,
Rensselaer Polytechnic Institute, Cairo University,
Rm. 207 Lally Building, Giza,
110 8th Street, Troy, NY 12180, USA. Egypt.
Amrit Pratap Yaser S. Abu-Mostafa
Department of Computer Science, Departments of EE and CS,
MC 136-93, MC 136-93,
Pasadena, CA 91125, USA. Pasadena, CA 91125, USA.
September 2, 2003
If X(t) is a random process on [0, T ], the maximum drawdown at time T , ŻD(T ), is defined by
ŻD(T ) = sup