Forward-backward systems for expected utility maximization

Ulrich Horst (1) , Ying Hu (2) , Peter Imkeller (1) , Anthony Réveillac (3) , Jianing Zhang (4)

1 Institut für Mathematik [Berlin]
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]

In this paper we deal with the utility maximization problem with a general utility function. We derive a new approach in which we reduce the utility maximization problem with general utility to the study of a fully-coupled Forward-Backward Stochastic Differential Equation (FBSDE).

Mots clés: Forward-Backward Stochastic Differential Equations; utility maximization

Domaines: Probabilités [math.PR]

Ulrich Horst, Ying Hu, Peter Imkeller, Anthony Réveillac, Jianing Zhang. Forward-backward systems for expected utility maximization. Stochastic Processes and their Applications, 2014, 124 (5), pp.1813-1848. ⟨10.1016/j.spa.2014.01.004⟩. ⟨hal-00631727⟩