Optimal investment: bounds and heuristics

Abstract

High-dimensional optimal investment/consumption problems are hard to deal with, not least because of the difficulty in characterizing the value function. This paper tries to offer ways to determine an approximately optimal policy, and to estimate its performance using duality methods. Though the value function is required as a concept in developing the theory, it plays no part in the computation, nor is it necessary to have global knowledge of the policy; it is enough to determine the policy along the realized sample path.