Schedule for Fall 2023
Seminars are on Thursdays
Time: 4:10pm – 5:25pm
Location: Room 903 SSW
Organizers: Steven Campbell, Ioannis Karatzas, Marcel Nutz, Philip Protter
9/14/23
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Jiacheng Zhang (Berkeley) Title: On time-consistent equilibrium stopping under aggregation of diverse discount rates. Abstract: This paper studies the central planner’s decision making on behalf of a group of members with diverse discount rates. In the context of optimal stopping, we work with a smooth aggregation preference to incorporate all heterogeneous discount rates with an attitude function that reflects the aggregation rule in the same spirit of ambiguity aversion in the smooth ambiguity preference proposed in Klibanoff et al.(2005). The optimal stopping problem renders to be time inconsistent, for which we develop an iterative approach using consistent planning and characterize all time-consistent equilibria as fixed points of an operator in the setting of one-dimensional diffusion processes. We provide some sufficient conditions on both the underlying models and the attitude function such that the smallest equilibrium attains the optimal equilibrium in which the attitude function becomes equivalent to the linear aggregation rule as of diversity neutral. When the sufficient condition of the attitude function is violated, we can illustrate by various examples that the characterization of the optimal equilibrium may differ significantly from some existing results for an individual agent, which now sensitively depends on the attitude function and the diversity distribution of discount rates.
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Date: Wednesday 9/20/23 Time: 2:40pm Location: 1025 SSW |
Martin Larsson (CMU) Title: Abstract:
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9/21/23
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Gilles Mordant (Göttingen/Yale) Title: Manifold learning with sparse regularised optimal transport. Abstract: In this talk, we discuss a method for manifold learning that relies on a symmetric version of the optimal transport problem with a quadratic regularisation. |
9/28/23
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Michael Ludkovski (UC Santa Barbara) Title: Machine Learning Surrogates for Parametric and Adaptive Optimal Execution Abstract : We investigate optimal order execution with dynamic parametric uncertainty. Our base model features discrete time, stochastic transient price impact generalizing Obizhaeva and Wang (2013). We first consider learning the optimal strategy across a multi-dimensional range of model configurations, including price impact and resilience parameters, as well as initial stochastic states. We develop a numerical algorithm based on dynamic programming and deep learning, utilizing an actor-critic framework to construct two neural-network (NN) surrogates for the value function and the feedback control. We then apply the lens of adaptive robust stochastic control to consider online statistical learning of model parameters along with a worst-case min-max optimization. Thus, the controller is dynamically learning model parameters based on her observations while explicitly accounting for Bayesian uncertainty of the learned parameter estimates via a posterior uncertainty set. We propose a modeling framework which allows a time-consistent 3-way marriage between dynamic learning, dynamic robustness and dynamic control. We extend our NN approach to tackle the resulting 7-dimensional adaptive robust optimal order execution problem, and illustrate with comparisons to alternative frameworks, such as adaptive or static robust strategies. This is joint work with Moritz Voss (UCLA) and Tao Chen (QRM). |
10/5/23
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Professor: Steven Campbell (Columbia) Title: Macroscopic Properties of Large Equity Markets and Relative Arbitrage under Transaction Costs Abstract: This talk investigates the macroscopic properties of the US equity market, spotlighting both well-established stylized facts and recent findings. In financial econometrics and empirical asset pricing, a great deal has been discovered about the statistical properties of individual assets at low and high frequencies. By comparison, relatively little attention has been paid to large-scale features such as the capital distribution curve. These macroscopic objects are central to the sub-field of mathematical finance known as Stochastic Portfolio Theory (SPT). A cornerstone of SPT is the concept of relative arbitrage, which is established under mild assumptions on market diversity and volatility. We discuss some implications of the presented stylized facts on the construction of realistic stochastic models and consider their influence on portfolio performance. Additionally, we integrate proportional transaction costs into the SPT framework by building on the recent work of Ruf (2020) and study the structure they impose. In the process, we explore how the original assumptions may be modified so that relative arbitrage can still exist. We close by empirically analyzing if these strengthened assumptions are justified in practice and investigating some portfolios that generate relative arbitrage in our expanded setting. This is joint work with Leonard Wong from the University of Toronto.
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10/12/23
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Sebastian Jaimungal (Toronto) Title: Inverse Reinforcement Learning with Dynamic Risk Measures
Abstract: This talk focuses on decision making under uncertainty when an agent assesses sequences of random costs using dynamic risk measures. The first part of the talk focuses on how an agent can control costs using reinforcement learning coupled with notions of conditional electability. The second part of the talk focuses on how a learner can design environments to elicit the risk preferences of the agent – with robo-advising being a primary application domain.
Based on joint works with Álvaro Cartea, Anthony Coache and Ziteng Cheng:
– Eliciting Risk Aversion with Inverse Reinforcement Learning via Interactive Questioning, working paper https://arxiv.org/abs/
– Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning, SIAM J. Financial Mathematics, Forthcoming https://arxiv.org/
– Reinforcement Learning with Dynamic Convex Risk Measures, Mathematical Finance https://onlinelibrary.
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10/19/23
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Leandro Sánchez-Betancourt (Oxford University) Title: Automated Market Makers Designs beyond Constant Functions Abstract: |
10/26/23
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Kevin Webster (Imperial College/Garden Leave from Citadel) Title: Unwinding Stochastic Orderflow Abstract: We extend optimal execution to stochastic order flows. Stochastic order flow arises in trading desks that aggregate order flows, such as Market Makers and Central Risk Books. The desk can warehouse in-flow orders, ideally netting them against subsequent opposite orders (internalization), or route them to the market (externalization) and incur costs related to price impact and bid-ask spread. We model and solve this problem for a general class of in-flow processes, enabling us to study how in-flow characteristics affect optimal strategy and core trading metrics. |
11/2/23
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Huyen Pham (Paris Cite) Title: Nonparametric generative modeling for time series via Schrödinger bridge Abstract: We propose a novel generative model for time series based on Schrödinger bridge (SB) approach. This consists in the entropic interpolation via optimal transport between a reference probability measure on path space and a target measure consistent with the joint data distribution of the time series. The solution is characterized by a stochastic differential equation on finite horizon with a path-dependent drift function, hence respecting the temporal dynamics of the time series distribution. We estimate the drift function from data samples by nonparametric, e.g. kernel regression methods, and the simulation of the SB diffusion yields new synthetic data samples of the time series. The performance of our generative model is evaluated through a series of numerical experiments. First, we test with autoregressive models, a GARCH Model, and the example of fractional Brownian motion, and measure the accuracy of our algorithm with marginal, temporal dependencies metrics, and predictive scores. Next, we use our SB-generated synthetic samples for the application to deep hedging on real data sets. Joint work with M. Hamdouche and P. Henry-Labordère. |
11/9/23 |
Johannes Wiesel (Carnegie Mellon University) Title: Martingale Schrödinger bridges Abstract: In a two-period financial market where a stock is traded dynamically, and European options at maturity are traded statically, we study the so-called martingale Schrödinger bridge Q∗; that is, the minimal-entropy martingale measure among all models calibrated to option prices. This minimization is shown to be in duality with an exponential utility maximization over semistatic portfolios. Under a technical condition on the physical measure P, we show that an optimal portfolio exists and provides an explicit solution for Q∗. This result overcomes the remarkable issue of non-closedness of semistatic strategies discovered by Acciaio, Larsson, and Schachermayer. |
11/16/23 |
NO SEMINAR |
11/23/23
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No Seminar (Thanksgiving) |
11/30/23 |
Jason Milionis (Columbia) Title: Quantifying Loss in Automated Market Makers (Loss-Versus-Rebalancing/LVR) Abstract: We consider the market microstructure of Constant Function Market Makers (CFMMs) from the economic perspective of passive liquidity providers (LPs). In a Black-Scholes setting with arbitrageurs trading against the liquidity pool and in the absence of fees, we decompose the return of an LP into an instantaneous market risk component and a non-negative, non-decreasing, and locally predictable component which we call “loss-versus-rebalancing” (LVR, pronounced “lever”). Even though market risk can be fully hedged, LVR remains as a running cost to LPs that must be offset by fee income in order for liquidity provision to be profitable. We show how LVR can be interpreted in many ways: as the cost of pre-commitment, as the time value for giving up future optionality, as the compensator in a Doob-Meyer decomposition, as an adverse selection cost in the form of the profits of arbitrageurs trading against the pool, and as an information cost because the pool does not have access to accurate market prices. LVR is distinct from the more commonly known metric of “impermanent loss” or “divergence loss”; this latter metric is more fundamentally described as “loss-versus-holding” and is not a true running cost. We express LVR simply and in closed form: instantaneously, it is the scaled product of the variance of prices and the marginal liquidity available in the pool. As such, LVR is easily calibrated to market data and specific CFMM structure. LVR provides tradeable insight in both the ex ante and ex post assessment of CFMM LP investment decisions, and can inform the design of CFMM protocols. This talk is based on joint work with Ciamac C. Moallemi (Columbia GSB), Tim Roughgarden (Columbia CS/a16z Crypto), and Anthony Lee Zhang (Chicago Booth). |
12/7/23 |
Rene Carmona (Princeton) Title: Model-Free Mean-Field Reinforcement Learning: Mean-Field MDP and Mean-Field Q-Learning Abstract: We study infinite horizon discounted Mean Field Control (MFC) problems with common noise through the lens of Mean Field Markov Decision Processes (MFMDP). We allow the agents to use actions that are randomized not only at the individual level but also at the level of the population. This common randomization allows us to establish connections between both closed-loop and open-loop policies for MFC and Markov policies for the MFMDP. In particular, we show that there exists an optimal closed-loop policy for the original MFC. Building on this framework and the notion of state-action value function, we then propose reinforcement learning (RL) methods for such problems, by adapting existing tabular and deep RL methods to the mean-field setting. The main difficulty is the treatment of the population state, which is an input of the policy and the value function. We provide convergence guarantees for tabular algorithms based on discretizations of the simplex. We also show that neural network based algorithms are more suitable for continuous spaces as they allow us to avoid discretizing the mean field state space. Numerical examples are provided.
Joint work with Mathieu Lauriere & Zongjun Tan
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