15:30
Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.
15:30
15:30
Identifying Bass martingales via gradient descent
Abstract
Brenier’s theorem and its Benamou-Brenier variant play a pivotal role
in optimal transport theory. In the context of martingale transport
there is a perfect analogue, termed stretched Brownian motion. We
show that under a natural irreducibility condition this leads to the
notion of Bass martingales.
For given probability measures µ and ν on Rn in convex order, the
Bass martingale is induced by a probability measure α. It is the min-
imizer of a convex functional, called the Bass functional. This implies
that α can be found via gradient descent. We compare our approach
to the martingale Sinkhorn algorithm introduced in dimension one by
Conze and Henry-Labordere.
How to choose a model? A consequentialist approach
Abstract
Mathematical modelling and stochastic optimization are often based on the separation of two stages: At the first stage, a model is selected out of a family of plausible models and at the second stage, a policy is chosen that optimizes an underlying objective as if the chosen model were correct. In this talk, I will introduce a new approach which, rather than completely isolating the two stages, interlinks them dynamically. I will first introduce the notion of “consequential performance” of each model and, in turn, propose a “consequentialist criterion for model selection” based on the expected utility of consequential performances. I will apply the approach to continuous-time portfolio selection and derive a key system of coupled PDEs and solve it for representative cases. I will, also, discuss the connection of the new approach with the popular methods of robust control and of unbiased estimators. This is joint work with M. Strub (U. of Warwick)
15:30
Stochastic optimal control and large deviations in the space of probability measures
Abstract
I will present problems a stochastic variant of the classic optimal transport problem as well as a large deviation question for a mean field system of interacting particles. We shall see that those problems can be analyzed by means of a Hamilton-Jacobi equation on the space of probability measures. I will then present the main challenge on such equations as well as the current known techniques to address them. In particular, I will show how the notion of relaxed controls in this setting naturally solve an important difficulty, while being clearly interpretable in terms of geometry on the space of probability measures.
15:30