A Review of Perturbative Approaches for Robust Optimal Portfolio Problems

Abstract

Only a few intertemporal optimal consumption and portfolio problems in partial and general equilibrium can be solved explicitly. It is illustrated in the paper that perturbation theory is a powerful tool for deriving approximate analytical solutions for the desired optimal policies in problems where general state dynamics are admitted and a preference for robustness is present. Starting from the perturbative approach proposed recently by Kogan and Uppal it is demonstrated how robust equilibria for some formulations of a preference for robustness in the literature can be solved. A crucial requirement for this approach is the existence of a known functional form for the candidate model solutions, a condition which is not satisfied by some models of a preference for robustness. For these cases,