Robust mean variance optimization problem under Renyi divergence information

In this paper, we consider the robust mean variance optimization problem where the probability distribution of assets' returns is multivariate normal and the uncertain mean and covariance are controlled by a constraint involving Renyi divergence. We present the closed-form solutions for the robust mean variance optimization problem and find that the choice of order parameter which is related to the Renyi divergence measure will not impact optimal portfolio strategy under the cases that the mean vector and the covariance matrix are uncertain, respectively. Moreover, we obtain the closed-form solution for the robust mean variance optimization problem under the case that the mean vector and the covariance matrix are both uncertain. We illustrate the efficiency of our results with an example.