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Mathematical Problems in Engineering
Volume 2017, Article ID 8249026, 10 pages
https://doi.org/10.1155/2017/8249026
Research Article

Uncertain Portfolio Selection with Background Risk and Liquidity Constraint

School of Economics and Management, Beihang University, Beijing 100191, China

Correspondence should be addressed to Jia Zhai; moc.anis@511198aijiahz

Received 8 October 2016; Revised 29 November 2016; Accepted 14 December 2016; Published 22 January 2017

Academic Editor: Thomas Hanne

Copyright © 2017 Jia Zhai and Manying Bai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper discusses an uncertain portfolio selection problem with consideration of background risk and asset liquidity. In addition, the transaction costs are also considered. The security returns, background asset return, and asset liquidity are estimated by experienced experts instead of historical data. Regarding them as uncertain variables, a mean-risk model with background risk, liquidity, and transaction costs is proposed for portfolio selection and the crisp forms of the model are provided when security returns obey different uncertainty distributions. Moreover, for better understanding of the impact of background risk and liquidity on portfolio selection, some important theorems are proved. Finally, numerical experiments are presented to illustrate the modeling idea.