Professor Pieter Allaart invites you to attend the PhD dissertation defense of Jose Islas this Thursday, October 22nd, at 3:30 pm in GAB 461. Cake and coffee will be served in GAB 472 following this event.
"Sharp lower bounds for stopping at or near the top of a sequence"
Abstract:
A gambler will observe a finite sequence of continuous random variables. After he observes a value he must decide to stop or continue taking observations. He can play two different games A) Win at the maximum or B) Win within a proportion of the maximum. In the first part of this talk the sequence to be observed is independent. We show that for each n>1, the optimal win probability in game A is bounded below by (1-1/n)^{n-1}. We accomplish this by reducing the problem to that of choosing the maximum of a special sequence of two-valued random variables and applying the sum-the-odds theorem of Bruss (2000).
Secondly, we assume the sequence is i.i.d. We provide the best lower bounds for the winning probabilities in game B given any continuous distribution. These bounds are the optimal win probabilities of a game A which was examined by Gilbert and Mosteller (1966).