Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints

Abstract

We develop a dual-control method for approximating investment strategies in incomplete environments that emerge from the presence of trading constraints. Convex duality enables the approximate technology to generate lower and upper bounds on the optimal value function. The mechanism rests on closed-form expressions pertaining to the portfolio composition, from which we are able to derive the near-optimal asset allocation explicitly. In a real financial market, we illustrate the accuracy of our approximate method on a dual CRRA utility function that characterises the preferences of a finite-horizon investor. Negligible duality gaps and insignificant annual welfare losses substantiate accuracy of the technique.

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

JEL Classification: D52, D53, G11