# Lecture Series

**Venue:** HIM lecture hall, Poppelsdorfer Allee 45

Optimal stopping problems: Basic formulations, concepts and methods of solution

Monday, May 13 and Tuesday, May 14

15:00-16:00 Lecture: Albert Shiryaev

16:00-16:30 tea break

16:30-17:30 Lecture: Albert Shiryaev

Tuesday, May 21 and Wednesday, May 22

15:00-16:00 Lecture: Mikhail Zhitlukhin

16:00-16:30 tea break

16:30-17:30 Lecture: Mikhail Zhitlukhin

Outline

In the first part of the lectures we give:

- Standard and non-standard optimal stopping problems.
- Connection of optimal stopping problems with the PDE theory.
- Examples of solutions of optimal stopping problems and free-boundary problems.
- Martingale and Markov methods of the general optimal stopping theory.

The second part of the lectures discusses:

- Stochastic problems of mathematical finance and sequential analysis.
- Reduction to Markovian optimal stopping problems and free-boundary problems.

The Monge-Kantorovich Problem

Monday, June 10 and Tuesday, June 11

15:00-16:00 Lecture: Alexander Kolesnikov

16:00-16:30 tea break

16:30-17:30 Lecture: Alexander Kolesnikov

Outline

The course of lectures will review the rich and elegant theory associated with the Monge-Kantorovich mass transfer problem. In the last two decades this theory was developing rapidly and has been fruitfully employed in various fields of applied mathematics, including economic modeling. The first part of the course (Lectures 1 and 2) will introduce into the subject, and the second part (Lectures 3 and 4) will present a more advanced material related to cutting edge research in the field.

Unbeatable Strategies

Thursday, June 13 and Friday, June 14

15:00-16:00 Lecture: Yurii Khomskii

16:00-16:30 tea break

16:30-17:30 Lecture: Yurii Khomskii

Outline

In this course, we present a mathematical framework for the study of "two-person, perfect information, zero sum games", of finite or infinite length. We focus on the existence of winning strategies, i.e., algorithms for a given player which making sure that, no matter what the opponent plays, the game will result in a win for the given player. A central concept is "determinacy", or the existence of a winning strategy for one of the two players.

In the first part of the course, we will focus on the classical theory of finite and infinite games, roughly following its early history (Zermelo, König, Kalmar, Gale-Stewart). In the second part, we will look at some more advanced applications of (mostly infinite) games in analysis, topology and set theory.

Introduction to the theory of evolutionary games: Part II

Monday, July 8

15:00-16:00 Lecture: Josef Hofbauer (Univ of Vienna)

16:00-16:30 Tea break

16:30-17:30 Lecture: Josef Hofbauer (Univ of Vienna)

Outline

This lecture will provide a self-contained and general-interest introduction to the theory of evolutionary games and its applications.