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

Nicole El Karoui (1, 2) , Mohamed M'Rad (3, 1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 LAGA - Laboratoire Analyse, Géométrie et Applications

The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making minimal assumptions and convex constraints on test-processes, we construct by composing two stochastic flows of homeomorphisms, all the consistent stochastic utilities whose the optimal-benchmark process is given, strictly increasing in its initial condition. Proofs are essentially based on stochastic 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-00477380v2⟩