Optimal position targeting via decoupling fields - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Optimal position targeting via decoupling fields

Résumé

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.
Fichier principal
Vignette du fichier
position_targeting_via_decoupling_fields.pdf (575.28 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01500311 , version 1 (03-04-2017)
hal-01500311 , version 2 (16-04-2018)

Identifiants

  • HAL Id : hal-01500311 , version 1

Citer

Stefan Ankirchner, Alexander Fromm, Thomas Kruse, Alexandre Popier. Optimal position targeting via decoupling fields. 2017. ⟨hal-01500311v1⟩

Collections

FMPL
991 Consultations
392 Téléchargements

Partager

Gmail Facebook X LinkedIn More