Welcome to the 'Optimal Stopping and Related Fields Seminar,' organized by Steven Campbell, Georgy Gaitsgori, and Ioannis Karatzas.
The seminar meets in-person in Columbia University on Firdays at 4:45 pm in Math room 520.
This seminar is the logical continuation of the seminar held in Fall 2025 - Optimal Stopping Seminar - Fall 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 |
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| Friday, February 20, 4:45 pm | Karl Kristian Engelund (University of Copenhagen) | Quickest change-point detection in stochastic volatility models
Stochastic volatility models are widely used for modelling asset prices, but static parameters fail to capture sudden regime shifts. We consider the problem of detecting a change in the dynamics of the latent volatility process, occurring at a random time, upon sequential observations of the price process. The objective is to estimate the time of a parameter change as accurately as possible in an online procedure. While quickest detection problems of a change in drift of an observable process are well studied, due to Girsanov's theorem yielding a direct finite dimensional filter, online change-point detection of latent processes remain comparatively unexplored. Yet, a change in volatility is critical for applications to option pricing. We first analyse the oracle problem where the volatility process is directly observable, based on the realized variance. Then we turn to the partial information setting where the variance process is considered latent. This constitutes a double filtering problem, estimating the latent process and the change-point. We arrive at an infinite-dimensional, measure valued, optimal stopping problem, for which we propose a simple numerical algorithm. The numerical algorithm is tested against the realized variance and the oracle problem, which shows promising results. Finally, we dive deeper into the measure valued optimal stopping problems and consider possible extensions for the theory. This work is based on discussions with Richard A. Davis from Columbia and Kristoffer J. Glover from University of Technolo. |
| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, February 27, 4:45 pm | David Itkin (LSE) |
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| Friday, March 6, 4:45 pm | Richard Groenewald (Bank of America) |
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| Friday, March 13, 4:45 pm | Tiziano De Angelis (University of Torino) |
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| Friday, March 20, 4:45 pm | No seminar (Spring break) |
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| Friday, March 27, 4:45 pm | Nizar Touzi (NYU) |
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| Friday, April 3, 4:45 pm | Erhan Bayraktar (University of Michigan) |
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| Friday, April 10, 4:45 pm | Tomoyuki Ichiba (University of California Santa Barbara) |
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| Friday, April 17, 4:45 pm | Georgy Gaitsgori (Columbia University) |
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| Friday, April 24, 4:45 pm | Philip A. Ernst (Imperial College London) |
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| Friday, May 1, 4:45 pm | Ioannis Karatzas (Columbia University) |
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| Date and time | Speaker | Title and abstract |
|---|---|---|
| Friday, January 30, 12:15 pm | Goran Peskir (University of Manchester) | The Dubins constants for Walsh's spider process
A long-standing open problem of L. E. Dubins seeks to determine the maximal expected range of Walsh's spider process on n edges per root of the expected stopping time. The solution is known for n=1 (1988) and n=2 (2009). In this talk I will present the solution for n>=3. |
| Friday, February 6, 4:45 pm | Yuqiong Wang (University of Michigan) | Optimal match length in knock-out tournaments
In sports tournaments, later stage games such as the final are usually treated as more important. We ask ourselves if this intuition can be justified from a sequential testing perspective. We study a knock-out type of tournament with $2^n$ players, where the goal is to decide how long each game should be played to identify the best player. We model each match as a sequential testing problem of a Brownian motion, with its drift representing the players' relative abilities. We show that the optimal design allocates longer match lengths to later rounds. In addition, we quantify the efficiency gain of allowing such sequential decisions, compared to fixing match lengths in advance. |
| Friday, February 13, 4:45 pm | Steven Campbell (Columbia University) | A mathematical study of the excess growth rate
The excess growth rate is a fundamental concept in portfolio theory: it captures the profit of a portfolio due to rebalancing and quantifies the intrinsic volatility of a stock market. In this talk, we undertake an in-depth mathematical study of this object and explore its connections to familiar concepts in information theory like the relative, Renyi and cross entropies, the Helmholtz free energy, L. Campbell's measure of average code length, and large deviations. Our main results consist of three characterization theorems for the excess growth rate in terms of (i) the relative entropy, (ii) the gap in Jensen's inequality, and (iii) the logarithmic divergence which is a generalization of the Bregman divergence. We also discuss the maximization of the excess growth rate and compare it with the growth optimal portfolio. Our results not only provide theoretical justifications of its significance, but also establish new connections between information theory and quantitative finance. Based on joint work with Ting-Kam Leonard Wong. |