Welcome to the 'Optimal Stopping Seminar,' run by the students and postdocs of Columbia University.
The seminar meets in-person in Columbia University on Firdays at 5:00 pm in Math room 507.
This seminar is the logical continuation of the seminar held in Spring 2025 - Optimal Stopping Theory: Methods and Techniques - Spring 2025.
If you would like to come or to be added on the mailing list, please email gg2793@columbia.edu.
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, October 10, 5:00 pm | No seminar (Stony Brook probability day) |
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, October 17, 5:00 pm | Christian Fiedler | TBA
TBA |
| Friday, October 24, 5:00 pm | Raphael Grondin | TBA
TBA |
| Friday, October 31, 5:00 pm | Manuel Arnese | TBA
TBA |
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, September 19, 5:00 pm | Steven Campbell | A Tractable Triple Problem in Sequential Inference: Filtering, Control, and Stopping
We study a Bayesian sequential inference problem for the drift of a Brownian motion in which the observer not only chooses their stopping and decision rules, but also controls the rate at which information is acquired. This extension introduces a cost for information acquisition, transforming the classical formulation of Shiryaev (1967) into a joint problem of filtering, control, and optimal stopping. Problems of this kind arise in adaptive experimental design and real-time inference across domains such as healthcare, finance, and engineering, where information is costly and decision-making must be timely. Our framework accommodates a host of classification losses and general running costs on the control process. Despite the added complexity, the problem admits a remarkably simple and semi-explicit solution that exhibits structural parallels with the classical setting. This work highlights a rare instance in which a triple problem-combining inference, control, and stopping-remains analytically tractable. Based on joint work with Georgy Gaitsgori and Richard Groenewald. |
| Friday, September 26, 5:00 pm | Georgy Gaitsgori | An Optimal Stoping Problem with Drift Uncertainty
We consider an optimal stopping problem for a diffusion process whose drift is given by an unobservable Bernoulli random variable. The goal, unlike problems of sequential testing, is to stop the diffusion so as to minimize the terminal convex cost in the presence of the running cost per unit of elapsed time. We show that under suitable assumptions on the terminal cost (e.g., it is a power function), the problem admits a semi-explicit characterization. We also provide examples where the continuation region consists of multiple disjoint intervals. The talk is based on an ongoing project with Ioannis Karatzas. |
| Friday, October 3, 5:00 pm | Raphael Grondin | An introduction to entropy estimation in information theory (Part 1)
I will present the foundational results of Shannon, covering his famous Source Coding Theorem and Universal Codes. I will cover the celebrated Shannon-McMilan-Breiman theorem while motivating the famous result of Lempel and Ziv on estimating the entropy of a single ergodic source. If time permits, I will start presenting the theory for estimating the relative entropy of two given random sources \P, \Q and talk about the famous Wyner problem on waiting times and the various relative entropy estimation algorithms known and studied in the literature. |