# Multi-period mean–semivariance portfolio optimization based on uncertain measure

Multi-period mean–semivariance portfolio optimization based on uncertain measure In this paper, we discuss a multi-period portfolio selection problem when security returns are given by experts’ estimations. By considering the security returns as uncertain variables, we propose a multi-period mean–semivariance portfolio opti- mization model with real-world constraints, in which transaction costs, cardinality and bounding constraints are considered. Furthermore, we provide an equivalent deterministic form of mean–semivariance model under the assumption that the secu- rity returns are zigzag uncertain variables. After that, a modiﬁed imperialist competitive algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm. Keywords Multi-period portfolio optimization · Uncertain variable · Semivariance · Cardinality constraint · Imperialist competitive algorithm 1 Introduction a given expected value, or maximizing expected value for a given variance. Since then, variance is widely used as a Portfolio selection discusses the problem of how to allocate risk measure, and the mean–variance models are well investi- a certain amount of investor’s wealth among different assets gated such as Yoshimoto (1996), Best and Hlouskova (2000), and from a satisfying portfolio. The mean–variance (M–V) Liu et al. (2003), Corazza and Favaretto (2007), etc. How- model formulated by Markowitz http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Soft Computing Springer Journals

# Multi-period mean–semivariance portfolio optimization based on uncertain measure

, Volume OnlineFirst – Jun 2, 2018
17 pages

/lp/springer_journal/multi-period-mean-semivariance-portfolio-optimization-based-on-6bB89gUpWy
Publisher
Springer Berlin Heidelberg
Subject
Engineering; Computational Intelligence; Artificial Intelligence (incl. Robotics); Mathematical Logic and Foundations; Control, Robotics, Mechatronics
ISSN
1432-7643
eISSN
1433-7479
D.O.I.
10.1007/s00500-018-3281-z
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we discuss a multi-period portfolio selection problem when security returns are given by experts’ estimations. By considering the security returns as uncertain variables, we propose a multi-period mean–semivariance portfolio opti- mization model with real-world constraints, in which transaction costs, cardinality and bounding constraints are considered. Furthermore, we provide an equivalent deterministic form of mean–semivariance model under the assumption that the secu- rity returns are zigzag uncertain variables. After that, a modiﬁed imperialist competitive algorithm is developed to solve the corresponding optimization problem. Finally, a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm. Keywords Multi-period portfolio optimization · Uncertain variable · Semivariance · Cardinality constraint · Imperialist competitive algorithm 1 Introduction a given expected value, or maximizing expected value for a given variance. Since then, variance is widely used as a Portfolio selection discusses the problem of how to allocate risk measure, and the mean–variance models are well investi- a certain amount of investor’s wealth among different assets gated such as Yoshimoto (1996), Best and Hlouskova (2000), and from a satisfying portfolio. The mean–variance (M–V) Liu et al. (2003), Corazza and Favaretto (2007), etc. How- model formulated by Markowitz

### Journal

Soft ComputingSpringer Journals

Published: Jun 2, 2018

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