Optimal Portfolio in a Multiple-Priors Model

Abstract

This paper studies the maximization problem of utility from terminal wealth in a multiple-priors model, where asset prices are semimartingales. We first state the existence of a saddle-point for our problem, under some suitable conditions on the utility function and the set of priors, which gives the existence of a solution for the maximization problem. A second approach consists in solving a dual minimization problem over the supermartingale measures and different priors. We then consider the case of a Brownian filtration and study in detail the case of a Logarithmic utility function and the case of a Power utility function. Mathematics Subject Classification (2000). 93E20, 60J60, 47N1O.