Mathematical Finance Seminar Series

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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



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.


Date: Wednesday


Time: 2:40pm

Location: 1025 SSW

Martin Larsson (CMU)

A calibrated rank-based volatility stabilized model for the distribution of capital

The capital distribution curve of an equity universe relates the relative market capitalization of each stock to its rank within the universe. Within the framework of stochastic portfolio theory, we develop a model for the capital distribution curve and study its empirical performance. Our model is able to reproduce three key features of US equity data: (i) the long-term shape and stability of the capital distribution curve; (ii) volatilities of relative market capitalizations; and (iii) turnover rates among stocks, i.e., the frequency by which stocks switch ranks. We generate sample paths of the calibrated model and compare them to historical trajectories, both in and out of sample. Finally, we prove that our model exhibits relative arbitrage, which means that the market portfolio can be outperformed with probability one in bounded time. To the best of our knowledge, this is the first time a model admitting relative arbitrage has been shown to be empirically consistent with (i)-(iii) above. This is joint work with David Itkin.




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.
We show that the solution of such a problem yields a sparse and adaptive affinity matrix that can be interpreted as a generalisation of the bistochastic kernel normalisation.
We prove that the resulting kernel is consistent with a Laplace-type operator in the continuous limit, discuss geometric interpretations and establish robustness to heteroskedastic noise.
The performance on certain simulated and real data examples will be shown. Some open questions will be raised across the talk.




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).









Sebastian Jaimungal (Toronto)



Leandro Sánchez-Betancourt (King's College London)



Kevin Webster (Imperial College/Garden Leave from Citadel)



Huyen Pham (Paris Cite)







No Seminar (Thanksgiving)


Rene Carmona (Princeton)