Séminaire de Probabilités commun ICJ/UMPA

# Optimal position targeting via decoupling fields

## by Stefan Ankirchner

jeudi 15 mars 2018 de au (Europe/Paris)
at ICJ ( Fokko du Cloux )
 Description In the talk we consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing it, via a limiting argument, to an unconstrained control problem that consists in finding an absolutely continuous process minimizing the expected sum of the Lagrangian and the deviation of the terminal state from a given target position. Using the Pontryagin maximum principle one can characterize a solution of the unconstrained control problem in terms of a fully coupled forward-backward stochastic differential equation (FBSDE). We use the method of decoupling fields for proving that the FBSDE has a unique solution. The talk is based on joint work with Alexander Fromm, Thomas Kruse and Alexandre Popier. Documents: Autres occasions