Optimal position targeting via decoupling fields

  • Alexander Fromm (FSU Jena)
E1 05 (Leibniz-Saal)


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 we 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.

Katja Heid

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Benjamin Gess

Max-Planck-Institut für Mathematik in den Naturwissenschaften