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Robust multiobjective portfolio optimization: a set order relations approach

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Abstract

We consider Markowitz’s portfolio optimization problem that heavily suffers from uncertainties of input parameters. And based on set order relations, uncertain portfolio optimization problem at various extreme cases is modelled as robust multiobjective formulations. At first, borrowing set order relations, three concepts of set less ordered efficiency are defined for multiobjective portfolio optimization problems with uncertainties. Subsequently, following from Ben-Tal and Nemirovski (Math Oper Res 23(4):769–805, 1998; Oper Res Lett 25:1–13, 1999), several multiobjective robust counterparts are introduced, and tackled by multiobjective particle swarm optimization approach. As such, the properties of the obtained (robust) efficient solutions are further characterized. Finally, the empirical researches from the real stock market show that (robust) efficient solutions based on set order relations are highly advisable for the investors.

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Acknowledgements

The authors are grateful for financial support received from the 2015 Annual Natural Science Foundation (key projects) of the Department of Education of Sichuan Province (15ZA0383), the National Natural Science Foundation of China (71371157, 71671145), Ministry of Education of Humanities and Social Sciences Research Project (14YJC790008), the Humanities and Social Science Fund of the Ministry of Education (15YJA790031 and 16YJA790062), and the Young Scholar Fund of the Science and Technology Department of Sichuan Province (2015JQO010).

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Authors and Affiliations

  1. School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    Chen Chen

  2. School of Finance, Yunnan University of Finance and Economics, Kunming, 650221, People’s Republic of China

    Yu Wei

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  1. Chen Chen
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  2. Yu Wei
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Correspondence to Chen Chen or Yu Wei.

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I declare that I have no conflict of interests, financially or non-financially, directly or indirectly related to our work. There is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

Appendix

Appendix

See Table 3.

Table 3 Descriptive statistics of stock returns
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Chen, C., Wei, Y. Robust multiobjective portfolio optimization: a set order relations approach. J Comb Optim 38, 21–49 (2019). https://doi.org/10.1007/s10878-018-0364-9

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