Columbia-NYU Financial Engineering Colloquium: Mathias Beiglböck & David Itkin

The RSVP form will close on February 25th at 11:59 EST.

Mathias Beiglböck

Universität Wien

Title

A Brenier Theorem for measures on (P_2(... P_2(H) ...), W_2) and Applications to Adapted Transport

Abstract

We establish a Brenier theorem for iterated Wasserstein spaces. Specifically, for a separable Hilbert space H and N ≥ 1, we construct a full-support probability Λ in P_2^N(H) = P_2(... P_2(H) ...) that is transport regular: for all P, Q in P_2^N(H) with P << Λ, the W_2^2-optimal transport from P to Q is unique and of Monge type. In the first non-classical case N = 2 we show that optimal transports are given as the push-forward by the W_2-gradient (or Lions' derivative) of an L-convex function. To establish the result for general N we develop new adapted notions of Lions' lift, L-convexity and Lions' derivative. A key idea is a new identification between optimal-transport c-conjugation (with c given by maximal covariance) and classical convex conjugation on the lift.

A primary motivation comes from the adapted Wasserstein distance AW_2: our results yield a first Brenier theorem for AW_2 and characterize AW_2^2-optimal couplings through convex functionals on the space of L_2-processes.

Bio

Mathias Beiglboeck is a Professor at the University of Vienna, working on probability and mathematical finance with a particular focus on optimal transport and related problems; he previously held appointments at UC Berkeley, the University of Bonn, and The Ohio State University, and he received the FWF START Prize in 2014.

David Itkin

London School of Economics and Political Science

Title

The role of stochastic factors in ergodic robust growth optimization

Abstract

Drifts of asset returns are notoriously difficult to model accurately and, yet, trading strategies obtained from portfolio optimization are very sensitive to them. Nevertheless, practitioners allocate large resources to their estimation including through the construction of stochastic factors. To understand this interplay, we will study two general high-dimensional ergodic robust growth maximization problems under drift uncertainty, where the asset returns depend on untradeable stochastic factors. In the first problem, we additionally robustify over the dynamics of the factors, while in the second we assume their dynamics are known. The principal motivation of our work is pairs trading (and statistical arbitrage more generally) which will serve as the main example in this talk. Our main results characterize the robust growth-optimal strategy in both cases as solutions to explicit high-dimensional PDEs. However, the optimal strategies behave differently in the two frameworks, admitting a clear financial interpretation: stochastic factors can improve performance if one has good knowledge of their dynamics, but can otherwise deteriorate performance.

Bio

David Itkin is an Assistant Professor in the Statistics Department at the London School of Economics and Political Science (LSE). Prior to that he was a Chapman Fellow in Mathematics at Imperial College, where he remains an Honorary Lecturer. David holds a PhD in Mathematical Sciences from Carnegie Mellon University, obtained in 2022. He was recently named the 2026 Rising Star in Quant Finance by Risk.net for his work on price impact.