Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

A risk-sensitive control dual approach to a large deviations control problem

Auteur(s):

Code(s) de Classification MSC:

Résumé: We consider a control problem of an ergodic process where the objective is to maximize over long term the probability to overperform a given level. This is formulated as a large deviations control problem for which the standard dynamic programming methods may not be applied directly. We solve this problem by adopting a duality approach leading to a risk-sensitive ergodic control problem. In a continuous-time diffusion setting, we state a verification theorem in terms of partial differential equations for this dual problem. We then turn back to the primal problem by means of large deviations techniques. We derive the optimal rate function and nearly optimal controls for the large deviations optimization problem. Finally, explicit solutions are provided in a linear-quadratic case.

Mots Clés: Large deviations ; risk-sensitive control ; controlled diffusion ; Bellman equation ; duality

Date: 2002-02-06

Prépublication numéro: PMA-707