Optimal Dynamic Asset Allocation with Lower Partial Moments Criteria and Affine Policies

This paper discusses an optimization-based approach for solving multi-period dynamic asset allocation problems using empirical asymmetric measures of risk. Three features distinguish the proposed approach from the mainstream ones. First, our approach is non parametric, in the sense that it does not require explicit estimation of the parameters of a statistical model for the returns distribution: the approach relies directly on data (the scenarios) generated by an oracle which may include expert knowledge along with a standard stochastic return model. Second, it employs affine decision policies, which make the multi-period formulation of the problem amenable to an efficient convex optimization format. Third, it uses asymmetric, unilateral measures of risk which, unlike standard symmetric measures such as variance, capture the fact that investors are usually not averse to return deviations from the expected target, if these deviations actually exceed the target.