Solving non-linear portfolio optimization problems with interval analysis

Abstract

Estimation errors or uncertainities in expected return and risk measures create difficulties for portfolio optimization. The literature deals with the uncertainty using stochastic, fuzzy or probability programming. This paper proposes a new approach to treating uncertainty. By assuming that the expected return and risk vary within a bounded interval, this paper uses interval analysis to extend the classical mean-variance portfolio optimization problem to the cases with bounded uncertainty. To solve the interval quadratic programming problem, the paper adopts order relations to transform the uncertain programme into a deterministic programme, and includes the investors’ risk preference into the model. Numerical analysis illustrates the advantage of this new approach against conventional methods.

Keywords:

• portfolio selection
• interval analysis
• quadratic programming
• short selling

Acknowledgements

We are thankful for support from the No.71272160 and No.71172011 project of National Natural Science Foundation of China, No. NCET-12-0772 Program for New Century Excellent Talents in University of Ministry of Education of China and No. FRF-TP-09-022. A project of the Fundamental Research Funds for the Central Universities, this paper is finished as expected. We are also grateful to the anonymous referees for their professional comments and suggestions, which have greatly improved upon the earlier version of this paper.