Jean-François Chassagneux, Laboratoire de Probabilités, Statistique et Modélisation, Université Paris Cité.

A dual approach to partial hedging

We introduce a class of `weak hedging problem’ which contains as special examples the quantile hedging problem (Föllmer Leukert 1999) and PnL matching problem (introduced in Bouchard & Vu 2012).We show that they can generally be rewritten as a kind of Monge transport problem. Using this observation, we introduce a Kantorovich version of the problem and, in some cases, we are able to prove a dual formulation. This allows us to design numerical methods based on SGD algorithms to compute the weak hedging price.

This is joint work with C. Bénézet (ENSIIE) and M. Yang (Université Paris Cité).