Colloquium | Institute of Mathematical Sciences
Time：10:30-11:30, Dec. 28, Friday
Location：Room 302, Library
Speaker: Dr. Gaoyue Guo, Byrne Research Assistant Professor, University of MichiganAbstract : The martingale optimal transport (MOT) is motivated by, and contributing to, the so-called robust pricing of exotic options which addresses questions of practical importance in finance, especially in the wake of financial crisis. As the optimizer of MOT problems in general dimensions is still not fully elucidated, i.e. lack of explicit formula and analytical characterization, it becomes increasingly important to develop numerical solution techniques for these problems given their active theoretical interest and significance for applications in mathematical finance. We prove that, a general multi-step multi-dimensional MOT problem can be approximated through a sequence of linear programming (LP) problems which result from a discretization of the marginal distributions combined with a suitable relaxation of the martingale condition. Specializing to the one-step model on real line, Kantorovich's duality yields an estimation of the convergence rate. Furthermore, we provide two generic discretization approaches of probability measures, deterministic and stochastic, which finally lead to a complete scheme for MOT problems.