# Mean-TVaR Models for Diversified Multi-period Portfolio Optimization with Realistic Factors based on Uncertainty Theory

### Abstract

The focus of any portfolio optimization problem is to imitate the stock markets and propose the optimal solutions to dealing with diverse investor expectations. In this paper, we propose new multi-period portfolio optimization problems when security returns are uncertain variables, given by experts’ estimations, and take the Tail value at risk (TVaR) as a coherent risk measure of investment in the framework of uncertainty theory. Real- constraints, in which transaction costs, liquidity of securities, and portfolio diversification, are taken into account. Equivalent deterministic forms of mean–TVaR models are proposed under the assumption that returns and liquidity of the securities obey some types of uncertainty distributions. We adapted the Delphi method in order to evaluate the expected, the standard deviation and the turnover rates values of returns of the given securities. Finally, numerical examples are given to illustrate the effectiveness of the proposed models.### References

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*Statistics, Optimization & Information Computing*,

*11*(4), 963-977. https://doi.org/10.19139/soic-2310-5070-1657

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