Solving non-linear portfolio optimization problems with interval analysis

Xiaoning Xu, Feng He, Rong Chen and Qingzhi Zhang
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Xiaoning Xu: University of Science & Technology Beijing, Beijing, P.R. China
Feng He: University of Science & Technology Beijing, Beijing, P.R. China
Rong Chen: Tsinghua University, Beijing, P.R. China
Qingzhi Zhang: Tsinghua University, Beijing, P.R. China

Journal of the Operational Research Society, 2015, vol. 66, issue 6, 885-893

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.

Date: 2015
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