Uncertain random enhanced index tracking for portfolio selection with parameter estimation and hypothesis test

Abstract

The enhanced index tracking is an effective method for portfolio optimization that focuses on imitating the behavior of a special benchmark and achieving an excess return. In addition, uncertainty and randomness are two intrinsic attributes of real world systems. In this paper, we study an uncertain random enhanced index tracking for portfolio optimization with parameter estimation and hypothesis test based on chance theory, which combines uncertainty theory and probability theory. First, we formulate an uncertain random mean–variance enhanced index tracking model including both random risky securities and uncertain risky securities. Then the presented model is transformed into a quadratic programming problem and the analytical solutions are derived for some special cases. Furthermore, the uncertain hypothesis test is applied to examine the correctness of the unknown parameters solved by uncertain parameter estimation. Finally, three numerical simulations are presented for showing the applicability of the formulated models and the effectiveness of the enhanced index tracking strategies.