Optimal Stopping Reading Seminar

Summer 2021

Welcome to the Optimal Stopping Reading Seminar, run by the students of Columbia University.

This summer we will be studying Optimal Stopping Theory. We are going to read various books and papers, in particular Optimal Stopping and Free-Boundary Problems by Peskir and Shiryaev, and different papers by Karatzas. Our talks will be held over Zoom on Thursdays from 1p.m. to 2p.m. EDT.

If you would like to come or to be added on the mailing list, please email ggaitsgori@math.columbia.edu.

Past Seminars

Date and time Speaker Title and abstract
Thursday, May 20, 1:00p.m. EDT Georgy Gaitsgori On the secretary problem

We will discuss arguably the most famous optimal stopping problem -- the secretary problem (or dowry problem). We will discuss the problem, find the optimal strategy, and also find the asymptotic properties of such strategy. Then we will discuss the full-information extension of this problem, namely the case when all X_i come from a known distribution. If time permits, we will also briefly discuss some other extensions of the problem.
Thursday, May 27, 1:00p.m. EDT Xiang Fang Optimal stopping in discrete time

General optimal stopping theory in discrete time; Some examples; Application in American option pricing.
Thursday, June 3, 1:00p.m. EDT Gaozhan Wang The optimal stopping problem for the one-dimensional diffusion process

As a continued talk to the topic we had last time, the talk will show a new characterization of excessive functions for arbitrary one-dimensional regular diffusion processes, using the notion of concavity. It is shown that excessivity is equivalent to concavity in some suitable generalized sense. This permits a characterization of the value function of the optimal stopping problem as "the smallest nonnegative concave majorant of the reward function" and allows us to generalize the results of Dynkin and Yushkevich for standard Brownian motion.
Thursday, June 17, 1:00p.m. EDT No seminar.

Thursday, June 17, 1:00p.m. EDT Gaozhan Wang The optimal stopping problem for the one-dimensional diffusion process Part II - Applications on option pricing

As a continued talk to the topic we had last time, we will mainly discuss the application of optimal stopping theory to option pricing problem and specifically, pricing an "up-and-out" barrier put-option of American type under the Black-Scholes model. The talk will also include some warm-ups on options and financial derivatives.
Thursday, June 24, 1:00p.m. EDT No seminar.

Thursday, July 1, 1:00p.m. EDT Georgy Gaitsgori Optimal stopping in continuous time: basic notions and results in Markovian approach (OSFBP, Chapter 1.2.2)

We will start discussing the book Optimal Stopping And Free-Boundary Problems by G. Peskir and A. Shiryaev. In particular, we will discuss part 2.2 of chapter 1 about optimal stopping in continuous time under Markovian assumption. We will formally set the optimal stopping problem, introduce main definitions and notions, formulate main results and give some of the proofs.
Thursday, July 8, 1:00p.m. EDT No seminar.

Thursday, July 15, 1:00p.m. EDT Hindy Drillick Optimal Stopping and PDE (OSFBP, Chapter 3)

We will explore the connection between optimal stopping and PDEs following Chapter 3 of the book.
Thursday, July 22, 1:00p.m. EDT No seminar.

Thursday, July 29, 1:00p.m. EDT No seminar.

Thursday, August 5, 1:00p.m. EDT Lane Chun Yeung Principles of Smooth and Continuous Fit

We will discuss the principle of smooth fit and the principle of continuous fit, following Chapter 4 (Sections 8 and 9) of the book.

Continuation of the seminar - OS Seminar, Fall 2021.