Long time asymptotics for optimal investment

Huyen Pham (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CREST - Centre de Recherche en Économie et Statistique

This survey reviews portfolio selection problem for long-term horizon. We consider two objectives: (i) maximize the probability for outperforming a target growth rate of wealth process (ii) minimize the probability of falling below a target growth rate. We study the asymptotic behavior of these criteria formulated as large deviations control pro\-blems, that we solve by duality method leading to ergodic risk-sensitive portfolio optimization problems. Special emphasis is placed on linear factor models where explicit solutions are obtained.

Mots clés: ergodic HJB equation; Long-term investment; large deviations; risk-sensitive control; ergodic HJB equation.

Domaines: Gestion de portefeuilles [q-fin.PM]; Probabilités [math.PR]

Huyen Pham. Long time asymptotics for optimal investment. 2014. ⟨hal-01058657⟩