Maximum Drawdown of a Brownian Motion and AlphaBoost: a Boosting Algorithm

Citation

Pratap, Amrit (2004) Maximum Drawdown of a Brownian Motion and AlphaBoost: a Boosting Algorithm. Master's thesis, California Institute of Technology. doi:10.7907/J2H0-XV66. https://resolver.caltech.edu/CaltechETD:etd-05272004-115820

Abstract

We study two problems, one in the field of computational finance and the other one in machine learning.

Firstly we study the Maximal drawdown statistics of the Brownian random walk. We give the infinite series representation of its distribution and consider its expected value. For the case when drift is zero, we give an exact expression of the expected value and for the other cases, we give an infinite series representation. For all the cases, we compute the limiting behavior of the expected value.

Secondly, we propose a new algorithm for boosting, AlphaBoost, which does better than AdaBoost in reducing the cost function. We study its generalization properties and compare it to AdaBoost. However, this algorithm does not always give better out-of-sample performance.

Thesis Files