Cardinality constrained portfolio selection problem: A completely positive programming approach

Ye Tian; Shucherng  Fang; Zhibin Deng; Qingwei Jin

doi:10.3934/jimo.2016.12.1041

Article Contents

2016, Volume 12, Issue 3: 1041-1056. Doi: 10.3934/jimo.2016.12.1041

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Cardinality constrained portfolio selection problem: A completely positive programming approach

1.
School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130
2.
Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, NC 27606
3.
School of Management, University of Chinese Academy of Sciences, Beijing, 100190
4.
Department of Management Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310058

Received: February 28, 2014

Revised: April 30, 2015

Published: June 2016

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Abstract

In this paper, we propose a completely positive programming reformulation of the cardinality constrained portfolio selection problem. By constructing a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones, an $\epsilon$-optimal solution of the original problem can be found in finite iterations using semidefinite programming techniques. In order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can find better approximate and feasible solutions than other known methods in the literature.

Keywords:

Cardinality constrained portfolio selection problem,
completely positive programming,
second-order cone,
adaptive approximation.

Mathematics Subject Classification: Primary: 90C26, 90C59, 90C22; Secondary: 30E10.

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