Financial/Actuarial Mathematics Seminar

A classical result of Strassen asserts that given probabilities $\mu,\nu$ on the real line which are in convex-decreasing order, there exists a \emph{supermartingale coupling} with these marginals, i.e.\ a random vector $(X_1,X_2)$ such that $X_1\sim\mu$, $X_2\sim\nu$ and $\mathbb{E}[X_2\lvert X_1]=X_1$. However, it is a non trivial problem to construct particular solutions to this problem. In this talk we introduce a family of such supermartingale couplings, each of which admits canonical characterization in terms of stochastic dominance. As particular elements of this family we recover the increasing and decreasing supermartingale couplings that solve the supermartingale optimal transport problem for particular cost functions. This is a joint work with Erhan Bayraktar and Shuoqing Deng. Speaker(s): Dominykas Norgilas (UM)