Statistiskt seminarium

Abstrakt finns enbart på engelska: During the last decade there has been a rapid development of methods for computationally addressing optimal transport problems; motivated by applications within robust finance, effort has also been made to generalize some of these techniques to problems equipped with an additional martingale constraint. Computationally solving multi-marginal martingale optimal transport problems remains a challenging task though, particularly for problems formulated with a large number of marginals.

In this talk I will give a brief introduction to the martingale optimal transport problem and motivate why it is interesting from a mathematical finance point of view, before presenting an efficient framework for solving a class of such multi-marginal problems computationally. The method combines the celebrated entropic regularization with the exploitation of certain structures inherent in the problem, enabling fast computation of the optimal dual variables. I will also provide some examples that demonstrates the utility of our method in terms of computing model-independent bounds on the fair price of some exotic options, such as lookback options and Asian options. The talk is based on joint work with Sigrid Källblad and Johan Karlsson.