Constrained mean-variance portfolio optimization for jump-diffusion process under partial information

Abstract

This article studies a mean-variance portfolio selection problem for a jump-diffusion model, where the drift process is modulated by a continuous unobservable Markov chain. Since there is a constraint on wealth, we tackle this problem via the technique of martingale. We first investigate the full information case that the Markov chain can be observable, closed-form expressions not only for the optimal wealth process and optimal portfolio strategy but for the efficient frontier are derived. Then, by the filtering theory, we reduce the original partial information problem to a full information one, and the corresponding optimal results are obtained as well. Furthermore, if short selling is not allowed, we find that the solution in the full information case can be derived by transforming the problem into an equivalent one with constraint only on wealth, but this technique is not applicable anymore for the partial information case.