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Tuesday, October 20, 2026 4:00 pm - 5:00 pm EDT (GMT -04:00)

Distinguished Lecture by Erhan Bayraktar

David Sprott Distinguished Lecture Series

Erhan Bayraktar
Professor of Mathematics & Susan M. Smith Professor
Director of the Quantitative Finance and Risk Management Masters Program
Department of Mathematics
University of Michigan

Room: DC 1302

Analytical Approach to Continuous-Time Causal Optimal Transport

We study continuous-time causal optimal transport with a Markovian cost, coupling a finite-state Markov source with a diffusion target. By representing the source through its conditional distribution given observations of the target, we characterize the transport value using a fully nonlinear parabolic master equation on an enlarged state space. We also establish equivalence with two stochastic control formulations on the probability simplex: a controlled Kushner–Stratonovich filtering equation subject to a zero-mean condition, and a state-constrained stochastic control problem. These formulations lead to implementable numerical schemes that approximate the value from above and below.

This is joint work with Julio Backhoff, Ibrahim Ekren, and Antonios Zitridis.