DynOpt: Incorporating dynamics into mean-variance portfolio optimization

Mean-variance (MV) portfolio theory leads to relatively simple and elegant numerical problems. Nonetheless, the approach has been criticized for treating the market parameters as if they were constant over time. We propose a novel convex optimization problem that extends an existing MV formulation with chance constraint(s) by accounting for the portfolio dynamics. The core idea is to consider a multiperiod scenario where portfolio weights are implicitly regarded as the output of a state-space dynamical system driven by external inputs. The approach leverages a result on realization theory and uses the nuclear norm to penalize complex dynamical behaviors. The proposed ideas are illustrated by two case studies.