An explicit optimal control approach for mean-risk dynamic portfolio allocation

In this paper we develop a framework based on coherent risk measures and multiparametric programming for the formulation and solution of multi-stage stochastic optimization problems that arise in the context of dynamic portfolio allocation. To address mean-risk trade-off we use a mean-risk function based on CV@R. We show that this risk measure inherits coherence of CV@R. We then develop dynamic programming equations for the problem and show that the explicit feedback control law can be obtained via solving a sequence of multiparametric linear programs.