Professor Allaart invites you to attend the PhD dissertation defense of Edmond Brophy
"Prophet Inequalities for Multivariate Random Variables with Cost for Observations"
In prophet problems, two players with different levels of information make decisions to optimize their return from an underlying optimal stopping problem. The player with more information is called the "prophet" while the player with less information is known as the "gambler." In this presentation, as in the majority of the literature on such problems, we assume that the prophet is omniscient, and the gambler does not know future outcomes when making his decisions. Certainly, the prophet will get a better return than the gambler. But how much better? The goal of a prophet problem is to find the least upper bound on the difference (or ratio) between the prophet's return, M, and the gambler's return, V. Most prophet problems in the literature compare M and V when prophet and gambler buy (or sell) one asset. In this presentation, we present new prophet problems where prophet and gambler optimize their return from selling two assets, when there is a fixed cost per observation. Sharp bounds for the problem on small time horizons will be given; for the n-day problem, rough bounds and a description of the distributions for the random variables that maximize M-V will be presented.
Cake and coffee will be served in GAB 472 following th event.