Near-Optimal Mean-Variance Controls under Two-time-scale Formulations and Applications

Although the mean-variance control was initially formulated for financial portfolio management problems in which one wants to maximize expected return and control the risk, our motivations also stem from highway vehicle platoon controls that aim to maximize highway utility while ensuring zero accident. This paper develops near-optimal mean-variance controls of switching diffusion systems. To reduce the computational complexity, with motivations from earlier work on singularly perturbed Markovian systems \cite{SethiZ94,Yin&Zhang,GZB}, we use a two-time-scale formulation to treat the underlying systems, which is represented by use of a small parameter. As the small parameter goes to 0, we obtain a limit problem. Using the limit problem as a guide, we construct controls for the original problem, and show that the control so constructed is nearly optimal.