Columbia HomeSchedule for Spring 2025
Seminars are on Thursdays
Time: 4:10 pm – 5:25 pm
Location: Room 903, 1255 Amsterdam Ave.
Building access currently requires CUID or advance notice. If you need to be added to the guest list, contact Steven Campbell ([email protected]).
Organizers: Steven Campbell, Ioannis Karatzas, Marcel Nutz, Philip Protter
| 1/23/2025 |
Tiziano De Angelis (Torino) Title: Linear-quadratic stochastic control with state constraints on finite-time horizon Abstract: We obtain a probabilistic solution to linear-quadratic optimal control problems with state constraints. A d-dimensional diffusion X must be linearly controlled in order to keep the time-space process (t,X) inside a suitable set C, while at the same time minimising an expected cost that depends on the state (t,X) and it is quadratic in the speed of the control exerted. (Joint work with Erik Ekstrom, University of Uppsala, Sweden) |
| 1/30/2025 |
No Seminar |
| 2/6/2025 |
Julio Backhoff-Veraguas (Vienna) Title: On the specific relative entropy between continuous martingales Abstract: The laws of two continuous martingales will typically be singular to each other and hence have infinite relative entropy. But this does not need to happen in discrete time. This suggests defining a new object, the specific relative entropy, as a scaled limit of the relative entropy between the discretized laws of the martingales. This definition goes all the way back to Nina Gantert’s PhD thesis, and in recent time Hans Foellmer has rekindled the study of this object by for instance obtaining a novel transport-information inequality. In this talk I will first discuss the existence of a closed formula for the specific relative entropy, depending on the quadratic variation of the involved martingales. Next I will describe an application of this object to prediction markets. Concretely, David Aldous asked in an open question to determine the ‘most exciting game’, i.e. the prediction market with the highest entropy. With M. Beiglbock we give a concise answer to this question. Finally, if time permits, I will give a glimpse to different extensions of this object, e.g. to higher dimensions or when we replace the role of the relative entropy by a power of the Wasserstein distance.
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2/13/2025 |
Marcus Wunsch (Zurich) – VIRTUAL TALK Title: Leveraging Constant Function Market Makers for decentralized portfolio management Abstract: In Decentralized Finance, anyone can serve as a market maker by providing liquidity to so-called liquidity pools. The exchange mechanism in such Decentralized Exchanges (DEX) is typically governed by a Constant Function Market Maker. I will discuss how, in the absence of transaction costs, weighted variance swaps hedge the adverse selection risk faced by liquidity providers due to arbitrage activities necessary for price discovery within a liquidity pool. On the other hand, if transaction fees are applied, liquidity provision resembles constant-weighted portfolio management under fairly mild assumptions, so that “Loss-Versus-Rebalancing” becomes a non-negative gain. The precise relationship between transaction fees and the resulting portfolio weights, however, remains an open question. Finally, I will present a recent result that explains in what sense the exchange mechanism of a Constant Product Market Maker with concentrated liquidity can be considered optimal. This is based on joint work with Masaaki Fukasawa (Osaka University) and Basile Maire (Quantena AG).
Steven Campbell is inviting you to a scheduled Zoom meeting. Topic: CUMF Seminar Meeting ID: 998 4795 9219 |
| 2/20/205 |
Haoyang Cao (Johns Hopkins) Title: Risk of Transfer Learning and its Applications in Finance Abstract: Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. In this paper, we propose a novel concept of transfer risk and analyze its properties to evaluate transferability of transfer learning. We apply transfer learning techniques and this concept of transfer risk to stock return prediction and portfolio optimization problems. Numerical results demonstrate a strong correlation between transfer risk and overall transfer learning performance, where transfer risk provides a computationally efficient way to identify appropriate source tasks in transfer learning, including cross-continent, cross-sector, and cross-frequency transfer for portfolio optimization. |
| 2/27/2025 |
Jose Figueroa-Lopez (WashU) Title: Adaptive Optimal Market Making Strategies with Inventory Liquidation Cost Abstract: A novel high-frequency market-making approach in discrete time is proposed that admits closed-form solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). The most important feature of our optimal placement strategy is that it can react or adapt to the behavior of market orders online. Using LOB data, we train our model and reproduce the anticipated final profit and loss of the optimal strategy on a given testing date using real LOB data. Our adaptive optimal strategies outperform the non-adaptive strategy and those that quote limit orders at a fixed distance from the midprice. We explore other extensions of the proposed approach. |
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3/6/2025 |
Christian Bayer (WIAS Berlin) Title: Signatures for stochastic optimal control Abstract: Models with memory play in increasingly important role in many applications, from finance to molecular dynamics. In a stochastic setting, memory means that the underlying stochastic process is not a Markov process. Such processes are particularly challenging for stochastic optimal control, as most state-of-the-art numerical methods for solving stochastic optimal controls problems heavily rely on the Markov property. Building on earlier works by Terry Lyons, we show that paths signatures allow us to efficiently solve several classes of stochastic optimal control problems even when the underlying state process is not a Markov process, We provide theoretical analysis and numerical applications, with special emphasis on Bermudan option pricing.
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3/13/2025 |
Xin Zhang (NYU Tandon)
Title: Exciting games and Monge-Ampère equations
Abstract: In this talk, we consider a competition between d+1 players, and aim to identify the “most exciting game” of this kind. This is translated, mathematically, into a stochastic optimization problem over martingales that live on the d-dimensional sub-probability simplex and terminate on the vertices of the simplex, with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Ampère equations, and identify the optimal martingale via a detailed analysis of boundary asymptotics of a Monge-Ampère equation.
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3/18/2025 SEMINAR STARTS AT 1:00 P.M. ROOM 1025 – SSW |
Julien Guyon (Paris Tech) SEMINAR WILL BE HELD IN ROOM 1025 Title: Fast Exact Joint S&P 500/VIX Smile Calibration in Discrete and Continuous Time Abstract: We introduce a novel discrete-time-continuous-time exact calibration method: we first build an S&P 500/VIX jointly calibrated discrete-time model that is later extended to continuous time by martingale interpolation. The benefit is that both steps can be made much faster than the known methods that directly calibrate a continuous-time model. We propose Newton-Sinkhorn and implied Newton algorithms that are much faster than the Sinkhorn algorithm that (Guyon, Risk, April 2020) used to build the first arbitrage-free model exactly consistent with S&P 500 and VIX market data. Using a (purely forward) Markov functional model, we then quickly build an arbitrage-free continuous-time extension of this discrete- time model. Additionally, new model-free bounds on S&P 500 options emphasize the value of the VIX smile information. Extensive numerical tests are conducted. This is joint work with Florian Bourgey. |
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3/20/2025 |
No seminar (spring break) |
| 3/27/2025 |
No seminar (Workshop: Statistics and Optimal Transport) THIS WILL BE HELD IN ROOM C03 (FLOOR – 1) AT 1255 AMSTERDAM AVENUE |
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4/3/2025 |
No seminar (Workshop: Optimization and Statistical Learning)
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4/10/2025 |
Ali Hirsa (Columbia) Title: Implementable AI in Asset Management: Under the Hood Abstract: Global assets under management are projected to reach $145 trillion by 2025. These assets span a wide spectrum of liquidity, tradability, and structural nuances. They vary in duration, are traded either on exchanges or by appointment, and involve diverse currencies, transaction frequencies, holding periods, protocols, and regulatory considerations—all of which generate a vast and complex pool of information. This complexity makes a strong case for AI-based decision processes. However, achieving meaningful AI implementation in nonstationary financial markets requires more than a simplistic “data in, miracles out” approach. It demands meticulous tuning, thoughtful enhancements, and, at times, a complete rethinking of standard methodologies. In this talk, we highlight our published AI advancements embedded within our AI-powered decision support system for asset management. |
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4/17/2025 |
Donghan Kim (KAIST) Title: Roughness in finance via Schauder Representation Abstract: This presentation will explain two distinct concepts for measuring the roughness of financial data. We first introduce the idea of the p-th variation of a real-valued continuous function along a general class of refining partition sequences. We demonstrate that the finiteness of the p-th variation of a given path is closely linked to the finiteness of the ℓp-norm of the coefficients along a Schauder basis, analogous to how the Hölder exponent relates to the ℓ∞-norm of the Schauder coefficients. This result establishes an isomorphism between the space of Hölder continuous functions with finite (generalized) p-th variation along a given partition sequence and a subclass of infinite-dimensional matrices, equipped with an appropriate norm, in the spirit of Ciesielski. |
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4/25/2025 Time: 1:00 p.m. Innovation Hub of Columbia Engineering (2276 12th Ave, New York, NY 10027) |
(Lars T. Nielsen Memorial Conference)
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5/1/2025 |
Valentin Tissot-Daguette (Bloomberg) Title: Occupied Processes: Unifying Path Dependence in Finance and Control Abstract: A stochastic process becomes “occupied” when it is enlarged with its occupation flow, tracking the time spent by the realized path at each level. We demonstrate that occupation flows provide a unified Markovian lift for exotic options, variance instruments, and stochastic control problems involving local times. We then derive an Itô formula for occupied processes, which lies midway between Dupire’s functional Itô formula and the classical one. A broad class of path-dependent PDEs is also unveiled through Feynman-Kac, with the occupation flow playing the role of time. Crucially, the space variable remains finite-dimensional, leading to a nearly classical proof of the comparison principle. We finally explore applications in financial modeling where volatility is driven by the occupied process, and highlight recent advances in the simulation of these models. This talk is partly based on joint work with Mete Soner (Princeton), Jianfeng Zhang (USC), and Xin Zhang (NYU). |
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