Fuzzy portfolio optimization for time-inconsistent investors: a multi-objective dynamic approach

  • You Li
  • Bo WangEmail author
  • Anrui Fu
  • Junzo Watada
Methodologies and Application


In recent years, fuzzy optimization has been widely adopted to handle the nonstatistical uncertainties in portfolio selection. Meanwhile, various risk measurements, including variance, entropy and value at risk, have been introduced in fuzzy environments to evaluate portfolio risks from different perspectives. In this study, we discuss fuzzy multi-objective dynamic portfolio optimization for time-inconsistent investors. When building the model, variance and value at risk as the representatives of different types of risk measurements are employed together with the expected return. And a dynamic investment policy is developed for time-inconsistent investors, which combines the expected return and value at risk into one objective. Then, the model is established to maximize the cumulative combined objective function and minimize the cumulative portfolio variance simultaneously. In addition, a multi-objective dynamic evolutionary algorithm is designed as a possible solution of the proposed model. The effectiveness of this research is demonstrated by using a real market data-based case study. Experimental results demonstrate that the proposed model matches the practical behavior of time-inconsistent investors and the solution algorithm is feasible to solve the complicated nonlinear problem.


Multi-objective dynamic optimization Portfolio selection Dynamic investment policy Fuzzy set theory Particle swarm optimization 



This work was supported by the National Natural Science Foundation of China (Grant No. 61603176), the Natural Science Foundation of Jiangsu Province (Grant No. BK20160632), the Young Scholar Support Programme of Nanjing University of Finance and Economics (Grant No. L_YXW15101) and the Fundamental Research Funds for the Central Universities (Grant No. 14380037).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of FinanceNanjing University of Finance and EconomicsNanjingChina
  2. 2.School of Management and EngineeringNanjing UniversityNanjingChina
  3. 3.Graduate School of Information, Production and SystemsWaseda UniversityKitakyushuJapan

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