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 analytically for the multi-period mean-variance-type portfolio selection problems

Mean-Variance Policy for Discrete-time Cone Constrained Markets: The Consistency in Efficiency and Minimum-Variance Signed Supermartingale Measure

The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed efficient policy may become inefficient when considering the corresponding truncated problem, thus stimulating investors' irrational investment behavior. We investigate analytically effects of portfolio constraints on time consistency of efficiency for convex cone constrained markets. More specifically, we derive the semi-analytical expressions for the pre-committed efficient mean-variance policy and the minimum-variance signed supermartingale measure (VSSM) and reveal their close relationship. Our analysis shows that the pre-committed discrete-time efficient mean-variance policy satisfies TCIE if and only if the conditional expectation of VSSM's density (with respect to the original probability measure) is nonnegative, or once the conditional expectation becomes negative, it remains at the same negative value until the terminal time. Our findings indicate that the property of time consistency in efficiency only depends on the basic market setting, including portfolio constraints, and this fact motivates us to establish a general solution framework in constructing TCIE dynamic portfolio selection problem formulations by introducing suitable portfolio constraints

Improving the Distribution of Densities in Southern California

Many of the biggest transportation challenges in Southern California arise not due to its overall density but due to the lack of concentration of densities. While recent years have witnessed increasing efforts to expand public transit services and encourage compact development in transit areas, there is a dearth of research providing support for improving the distribution of densities in the region. This project adopts a simultaneous equation modeling (SEM) approach to reveal the complexity of parcel-level (residential) land use intensification dynamics in a five-county Southern California metropolitan region with emphasis on the importance of reciprocal interactions between current and planned land use changes and the critical role of public transit accessibility. Results suggest that residential densification and upzoning processes reinforce each other. Urban residential upzoning can promote the probability of parcel-level residential densification significantly, even though it does not always lead to an immediate market response in every location. More importantly, the residential density increases are found to induce further plan/zoning modifications in nearby areas, indicating the presence of feedback loops in this dynamic relationship. There is also evidence of the positive influence of public transit accessibility. Single-family residential land parcels with greater access to high-quality transit services show a higher level of densification and upzoning probabilities, when all other conditions are held constant. Such positive effects are detected not only in existing high-quality transit areas but also in locations where public transit services will be available in the future