Robust mean variance optimization problem under Rényi divergence information. (1st February 2018)

• Record Type: Journal Article
• Authors: Ding, Ke-wei; Chen, Zhang-you; Huang, Nan-jing
• Is Part Of: Optimization. Volume 67:Number 2(2018)
• Page Start: 287
• Page End: 307
• Publication Date: 2018-02-01
• Subjects: Mean variance optimization problem -- robust optimization -- Rényi divergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1394298
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: 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 Rényi 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 Rényi 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.