Optimal investment and consumption with forward preferences and uncertain parameters

Abstract

We introduce and analyze a class of forward performance criteria in incomplete markets in the presence of model ambiguity. Incompleteness stems from general investment constraints, while model uncertainty is represented by a convex and compact set of plausible model parameter processes. Following the max-min criteria in traditional (backward) robust control, we formulate similar criteria for the robust forward performance processes and focus on the rich class of time-monotone processes. We provide a novel PDE characterization and a semi-explicit saddle-point construction of the robust forward performance criteria and their optimal policies. Furthermore, we present additional results within the class of homothetic constant relative risk aversion (CRRA) processes. Within this class, we investigate the relationship between forward performance processes on wealth and those on consumption, establishing an interesting dominance through time.