Investment Strategies Determined by Present Value Given as Trapezoidal Fuzzy Numbers

  • Krzysztof PiaseckiEmail author
  • Joanna Siwek
Conference paper
Part of the Springer Proceedings in Business and Economics book series (SPBE)


In the article, the present value is considered as a trapezoidal fuzzy number, same as obtained expected discount factor. The imprecise value of this factor may be used as a decision premise in creating new investment strategies. Considered strategies are built based on a comparison of a fuzzy profit index and the value limit. In this way, we obtain imprecise investment recommendation. Financial equilibrium criteria result from a special case of this comparison. Further in the paper, the following criteria are generalized: Sharpe’s ratio, Jensen’s alpha and Treynor’s ratio. Moreover, the safety-first criteria are generalized into the fuzzy case, along with Roy’s criterion, Kataoka’s criterion and Telser’s criterion. The obtained results show that the proposed theory can be used in investment applications.


Fuzzy imprecision Probabilistic uncertainty Return rate Expected discount factor Portfolio 



The article is financed by the National Science Centre, Poland, Grant No. 2015/17/N/HS4/00206.


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Authors and Affiliations

  1. 1.Department of Investment and Real EstatePoznan University of EconomicsPoznańPoland
  2. 2.Department of Imprecise Information Processing Methods, Faculty of Mathematics and Computer ScienceAdam Mickiewicz UniversityPoznańPoland

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