Optimal stochastic dominance through the lens of optimal transport
speaker: Karol Bolbotowski (Lagrange Mathematics and Computation Research Center, Paris)abstract: Consider the problem where for two centred probabilities we look for the third probability that dominates the other two in the convex order while exhibiting the minimal variance. Although falling within the scope of optimization in stochastic finance, this problem has emerged as a reformulation of an optimal design problem in structural mechanics. It also provides a new way of computing the second-order Zolotarev distance between two centred probabilities. After discussing these links, we will show how this optimal dominance problem can be tackled by a variant of optimal transport where, apart from the usual transport plan, we also look for a plan that is vector valued and whose marginals are moments of the target measures. This talk will cover two joint works: the first with Guy Bouchitté, and the second with Guillaume Carlier, Quentin Mérigot, and Filippo Santambrogio.
timetable:
Mon 2 Dec, 16:25 - 16:55, Aula Dini
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