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 FreeBoundary 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.
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 fullinformation 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 onedimensional 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 onedimensional 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 onedimensional 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 "upandout" barrier putoption of American type under the BlackScholes model. The talk will also include some warmups 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 FreeBoundary 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. 