2012 May 25 at 13:00
DC 1316
Shu Tong Tse, PhD candidate, David R. Cheriton School of Comp. Sci., Univ. Waterloo
We tackle the subtleties in applying the dynamic programming principle to non-convex multi-period mean variance optimization problems. For non-convex problems, the Lagrange multiplier method (e.g. Bielecki et al. 2005) cannot be applied and the embedding technique of Li and Ng (2000) has to be used. However, the embedding technique may yield solutions that are inefficient in the Pareto sense. Given the frontier computed by the embedding technique, we develop an algorithm that identifies all Pareto-efficient points obtainable using the weighted-sum scalarization approach. We also consider an optimal trade execution problem as an example. Our algorithm guarantees that the frontier computed using the embedding technique is the complete Pareto-efficient frontier.