Martingale Optimal Transport and Portfolio Theory

Abstract

This project involved the study of Monge-Kantorovich problem of optimally transporting one distribution of mass to another. A cost is incurred while doing the transportation and the optimality is measured against this cost function. The properties of solutions when the solution to optimal transport exist is studied. An application to portfolio theory, which amounts to finding a portfolio strategy, which depends only on the current state of the market, that will give the investor a possibility of unbounded profit with probability one. We study the dual version of Monge - Kantorovich problem for martingale measures which has a natural financial interpretation in terms of hedging options