Abstract
This paper applies axiomatic models of decision under ambiguity to the optimal portfolio choice problem with two objectives: firstly to account for the probabilistic model uncertainty, secondly to take into account the information contained in an observed sample of assets’ returns. Especially, a criterion is proposed which is a special case of the Variational Preferences. Restated in the Bayesian statistics notations, it is a regularized optimal problem which explores possible probabilistic models weighted by their likelihood given the observations. Examples and numerical simulations are provided to illustrate its properties, notably its robustness to misspecified models by comparing its performance to the benchmark portfolios of the literature. More generally, this paper aims to show that axiomatic models which have been developed to accommodate attitudes toward ambiguity provide a behavioral justification for aversion to model uncertainty in optimization problems, and lead to practical criteria which take into account the sample information.