\documentclass[12pt]{article}

\title{Detecting a regime change \& connections to mathematical
  finance}
\author{Olympia Hadjiliadis, Princeton University}
\date{April 17}

\begin{document}

\maketitle

\begin{abstract}

  The topic of statistical surveillance is presented. We begin by
  defining the out-of-control and in-control states of the process and
  describe how we can distinguish them by using statistics based on
  the observations of the process. In this context we present the
  CUSUM statistic. As an example of a problem in statistical
  surveillance we will present the topic of change-point detection in
  the Brownian motion model with multiple alternatives.  In this
  problem, the objective is to detect a change in the constant drift
  of a Brownian motion by means of a stopping rule that reacts fairly
  fast (with respect to a carefully selected criterion) to an abrupt
  change but at the same time keeps the frequency of false alarms
  above a certain threshold. In this context we also examine the
  specific instance of two-sided alternatives, where the two-sided
  CUSUM stopping rule (2-CUSUM) is employed.  We find the best 2-CUSUM
  stopping rule. We finally show very strong asymptotic properties of
  carefully chosen 2-CUSUM stopping rules.  We proceed to show
  connections of the 2-CUSUM process to two very important processes
  in finance the drawdown process and the rally process. We address
  the question of computing the probability that a drop of
  a\% from the running maximum of the underlying asset
  precedes a rally of b\% from the running minimum of the asset, under
  the assumption of the geometric Brownian motion dynamics governing
  the underlying asset. We conclude by discussing some open problems
  related to the above topics.
  
\end{abstract}




\end{document}

