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: TBD
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.
Erhan Bayraktar
Erhan Bayraktar is the Susan Meredith Smith Professor of Mathematics at the University of Michigan, where he also directs the Quantitative Finance and Risk Management Master’s Program. His research develops mathematical tools for decision-making under uncertainty, with contributions spanning stochastic analysis and control, applied probability, mean field games, mathematical finance, and machine learning. He leads a large and active research group and has mentored 17 doctoral students and more than 40 postdoctoral researchers. He has authored more than 200 publications and received honors including an NSF CAREER Award and the inaugural SIAG/FME Early Career Prize. He earned his Ph.D. from Princeton University in 2004.
David A. Sprott (1930-2013)
Professor David Sprott was the first Chair (1967-1975) of the Department of Statistics and Actuarial Science at the University of Waterloo and first Dean of the Faculty of Mathematics (1967-1972). The David Sprott Distinguished Lecture Series was created in recognition of his tremendous leadership at a formative time of our department, as well as his highly influential research in statistical science.
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