Professor Allaart invites you to attend the PhD Dissertation Defense of Zohreh Sharif Kazemi.

WHEN: Friday, June 11th, at 2:00pm

"Optimal Look-ahead Stopping Rules for Simple Random Walk"

ABSTRACT:

An optimal stopping problem is about picking the right time to do a known action based on sequentially observed random variables in order to maximize an expected return or to minimize an expected cost. In this type of problems, a real-time player decides to stop or continue at stage n based on the observations up to that stage. However, a prophet, who knows all steps ahead, can certainly achieve more by stopping on the largest reward. Prophet problems were first introduced by Krengel, Sucheston and Garling in 1977 and studied in depth by Hill and Kertz in the 1980s, and by many other authors afterwards. Although it is not really realistic to assume someone can foresee all the future values in a process, it may sometimes be possible to predict just a few further steps with a good accuracy, for instance think about insider trading. Therefore, another kind of prophet stopping rule problems emerges when we suppose a prophet knows just k steps ahead. We study several look-ahead stopping rule problems for simple random walk, including a simple random walk with finite horizon, a sum with negative drift problem and a discounted sum problem. We calculate the expected returns for a kstep look-ahead prophet, compare them with the real time case and derive upper bounds on the advantage of the prophet over the real time decision maker.