Robust mean variance optimization problem under Rényi divergence information

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.

Keywords:

• Mean variance optimization problem
• robust optimization
• Rényi divergence

Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11471230], [grant number 11671282], [grant number 11701478]; the Fundamental Research Funds for the Central Universities, Southwest Minzu University [grant number 2017NZYQN34].