Robust generalized Merton-type financial portfolio models with generalized utility

We include the notion of uncertainty and incomplete information within the classical Merton’s portfolio model. Incomplete information on the set of preferences is interpreted by means of a set-valued utility function. The model is formulated as set-valued optimization problems by construction. We provide scalarization techniques and equivalent formulations to reduce the complexity. The proposed models are robust with respect to noise induced by statistical estimation or data bias. Illustrative examples show how our new formulations work.