Schedule 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. |
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.
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2/13/2025 |
Speaker: 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. |
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. |
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. |
Speaker: Julien Guyon (Paris Tech) 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. |
3/20/2025 |
No seminar (spring break) |
3/27/2025 | No seminar (Workshop: Statistics and Optimal Transport) |
4/3/2025 |
No seminar (Workshop: Optimization and Statistical Learning)
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4/10/2025 |
Ali Hirsa (Columbia) Title: Abstract: |
4/17/2025 |
Donghan Kim (KAIST) Title: Abstract: |
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