1.Unified Framework of Mean-Field Formulations for Optimal Multi-period Mean-Variance Portfolio Selection

 The classical dynamic programming-based optimal stochastic control methods fail to cope with nonseparable dynamic optimization problems as the principle of optimality no longer applies in such situations. Among these notorious nonseparable problems, the dynamic mean-variance portfolio selection formulation had posted a great challenge to our research community until recently. A few solution methods, including the embedding scheme, have been developed in the last decade to solve the dynamic mean-variance portfolio selection formulation successfully. We propose in this paper a novel mean-field framework that offers a more efficient modeling tool and a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies for the multi-period mean-variance-type portfolio selection problems.

2. Selling Financial Assets at the Right Time

This paper studies a continuous-time market where an agent, having specified an investment horizon and a targeted terminal mean return, seeks to minimize the variance of the return. The optimal portfolio of such a problem is called mean-variance efficient Markowitz. It is shown that, under very mild conditions, a mean-variance efficient portfolio realizes the (discounted) targeted return on or before the terminal date with a probability greater than 0.8072. This number is universal irrespective of the market parameters, the targeted return, and the length of the investment horizon.