Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach
2022, Annals of Operations Research, 311, pp.1085–1098
Portfolio optimization
Set-valued probability
Imprecise probability
Set-valued optimization
Stochastic efficiency
Stochastic inefficiency
Abstract
In this paper we extend the notion of stochastic efficiency and inefficiency in portfolio optimization to the case of incomplete information by means of set-valued probabilities. The notion of set-valued probability models the concept of incomplete information about the underlying probability space and the probability associated with each scenario. Unlike other approaches in literature, our notion of inefficiency is introduced by means of the Monge–Kantorovich metric. We provide some numerical examples to illustrate this approach.