Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows

Nicole El Karoui (1, 2) , Mohamed M'Rad (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

The paper generalizes the construction by stochastic flows of consistent utilities processes introduced by M. Mrad and N. El Karoui (2010). The market is incomplete and securities are modeled as locally bounded positive semimartingales. Making minimal assumptions and convex constraints on test-portfolios, we construct by composing two stochastic flows of homeomorphisms, all the consistent stochastic utilities whose the optimal wealth process is a given admissible portfolio, strictly increasing in initial capital. Proofs are essentially based on change of variables techniques.

Mots clés: Consistent utilities; progressive utilities; forward utility; performance criteria; horizon-unbiased utility; consistent utility; progressive utility; portfolio optimization; optimal portfolio; duality; minimal martingal measure; Stochastic flows of homeomorphisms

Domaines: Finance quantitative [q-fin.CP]; Probabilités [math.PR]

Nicole El Karoui, Mohamed M'Rad. Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows. 2010. ⟨hal-00477380v1⟩