Near-Optimal Asset Allocation in Financial Markets with Trading Constraints

Abstract

We develop a dual-control method for approximating investment strategies in multidimensional financial markets with convex trading constraints. The method relies on a projection of the optimal solution to an (unconstrained) auxiliary problem to obtain a feasible and near-optimal solution to the original problem. We obtain lower and upper bounds on the optimal value function using convex duality methods. The gap between the bounds indicates the precision of the near-optimal solution. We illustrate the effectiveness of our method in a market with different trading constraints such as borrowing, short-sale constraints and non-traded assets. We also show that our method works well for state-dependent utility functions.

Keywords: Convex duality, incomplete markets, life-cycle investment, Malliavin calculus, state-dependent utility, stochastic optimal control

JEL Classification: D52, D53, G11