A linear reaction technique for dynamic asset allocation in the presence of transaction costs

Institutional investors manage their strategic mix of asset classes over time to achieve favorable returns in spite of uncertainties. A fundamental issue in this context is to maintain risk under control while achieving the desired return targets. When the asset mix is to be re-balanced many times over the investment horizon, the decision maker faces a rather difficult constrained dynamic optimization problem that should take into account conditional decisions based on future market behavior. This problem is usually solved approximately using scenario-based stochastic programming: a technique that suffers from serious problems of numerical complexity due to the intrinsic combinatorial nature of scenario trees. In this paper, we present a novel and computationally efficient approach to constrained discrete-time dynamic asset allocation over multiple periods. This technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon, and may account for proportional transaction costs and intertemporal dependence of the return process. A key feature of the proposed method is the introduction of a linearly-parameterized class of feedback reaction functions, which permits to obtain explicit analytic expressions for the portfolio statistics over time. These expressions are proved to be convex in the decision parameters, hence the multi-stage problem is formulated and solved by means of efficient tools for quadratic or second-order-cone convex programming.