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Transportation Problem with Stochastic Domination

Student: Timofey Zaytsev

Supervisor: Alexander Kolesnikov

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2021

This work is devoted to сertain results of the dominance theory for probability measures. The first part of the paper has an expository nature. It contains the following results: general facts about extreme points, special cases where extreme points can be found explicitly, and examples of orderings on a set of measures. As the main example, we analyze the result on extreme points on a set of measures with stochastic dominance. In the second part, we study a generalization of the classical Monge-Kantorovich transportation problem with stochastic domination. Our main result is an analog of the Kantorovich duality theorem for this problem.

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