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

OPTIMAL PORTFOLIO CONSTRUCTION BY MIXING HEDGE FUND

The returns of the hedge fund are declining in recent years, accompanying with the impact of the financial crisis in 2008. There will be a question that whether the hedge fund can still be used to blend in a conventional portfolio to improve the performance. Our paper focuses on the comparison analysis and does the basic asset allocation for the hedge fund and traditional portfolio. We analyze the risk-adjusted returns for conventional assets of US Equities, EAFE Equities, US Bonds and International Bonds as well as the hedge fund. Finally we find that, under current market condition, hedge fund is still an ideal alternative asset for the choice of the portfolio to increase the risk-adjusted return level

Decision Making under Cumulative Prospect Theory: An Alternating Direction Method of Multipliers

This paper proposes a novel numerical method for solving the problem of decision making under cumulative prospect theory (CPT), where the goal is to maximize utility subject to practical constraints, assuming only finite realizations of the associated distribution are available. Existing methods for CPT optimization rely on particular assumptions that may not hold in practice. To overcome this limitation, we present the first numerical method with a theoretical guarantee for solving CPT optimization using an alternating direction method of multipliers (ADMM). One of its subproblems involves optimization with the CPT utility subject to a chain constraint, which presents a significant challenge. To address this, we develop two methods for solving this subproblem. The first method uses dynamic programming, while the second method is a modified version of the pooling-adjacent-violators algorithm that incorporates the CPT utility function. Moreover, we prove the theoretical convergence of our proposed ADMM method and the two subproblem-solving methods. Finally, we conduct numerical experiments to validate our proposed approach and demonstrate how CPT's parameters influence investor behavior using real-world data.Comment: 30 page

Soft Actor-Critic Learning-Based Joint Computing, Pushing, and Caching Framework in MEC Networks

To support future 6G mobile applications, the mobile edge computing (MEC) network needs to be jointly optimized for computing, pushing, and caching to reduce transmission load and computation cost. To achieve this, we propose a framework based on deep reinforcement learning that enables the dynamic orchestration of these three activities for the MEC network. The framework can implicitly predict user future requests using deep networks and push or cache the appropriate content to enhance performance. To address the curse of dimensionality resulting from considering three activities collectively, we adopt the soft actor-critic reinforcement learning in continuous space and design the action quantization and correction specifically to fit the discrete optimization problem. We conduct simulations in a single-user single-server MEC network setting and demonstrate that the proposed framework effectively decreases both transmission load and computing cost under various configurations of cache size and tolerable service delay