# THEMATIC PROGRAMS

May 29, 2023

## Program in Probability and Its Applications Winter Kolmogorov Lecture Series

Tuesday, January 26, 1999
Hans Follmer (Humboldt Universitat - Berlin) Probabilistic Problems Arising From Finance

This lecture will be held at the ROM. Please see below. We review some recent developments in Probability which are motivated by problems of hedging derivatives in incomplete financial markets. This will include new variants of decomposition theorems for semimartingales, the construction of efficient hedges which minimize the shortfall risk under some cost constraint, and some results on Brownian motion related to the heterogeneity of information among financial agents.

*ROM Theatre is at 100 Queen's Park, Toronto. This lecture will be held during the Probability in Finance Workshop.

Tuesday, February 9, 1999
Burgess Davis (Purdue University) Perturbed and Reinforced Random Walks

Suppose we have two coins, one fair and the other with probability p of heads and 1-p of tails. Let X0, X1, X2, .... be the random walk constructed as follows. Put X0 = 0, and for n > 0, toss one of the coins to decide whether Xn is one greater (heads) or one less than Xn - 1. For the first jump (n= 1),make this toss with the fair coin. For the other jumps, toss the fair coin if min{Xk : k < n} < Xn-1 < max{Xk : k < n}, and otherwise toss the p coin. In other words, only use the p coin if the walker is at the edge of the interval of visited sites. If p is not equal to 1/2, the jump probabilities depend on the history of the walk, so the walk is not Markov, and many of the tools used to study fair random walk (the p = 1/2 case) are not applicable. I will discuss what is known about these and some related random walks.

Tuesday, March 23, 1999
Krzysztof Burdzy (University of Washington) Hot Bodies

Where is the hottest spot in a hot body? Is it on the surface or is it hidden below it? I will report on the more than skin deep research on these questions, performed jointly with R. Banuelos, W. Werner and R. Bass. The analytic results described were proved using a probabilistic coupling technique, previously developed in collaboration with W. Kendall for a statistically motivated project.