Investment management in uncertainty

  • A. Terceño
  • J. de Andrés
  • M. G. Barberà
  • T. Lorenzana
Part of the Applied Optimization book series (APOP, volume 55)


It is still not easy to define the content of the Financial Management of Companies but, even though we have no desire to create restrictions, we shall conceptualize it as the scientific discipline which attempts to optimally assign the scarce financial resources in a company both from the external and internal perspectives, that is to say, financial markets and financial management, respectively. This definition follows the most accepted meaning of Economy as the science which studies human behaviour as a relation between ends and scarce means which have alternative uses.


Interest Rate Cash Flow Fuzzy Number Investment Project Triangular Fuzzy Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. i.
    Suárez (1998, 28)Google Scholar
  2. ii.
    Femández (1991, 346–347)Google Scholar
  3. iii.
    Kaufrnarm and Gil (1986,70)Google Scholar
  4. iv.
    \(\mathop q\limits_ \sim\) and \(\mathop r\limits_ \sim\)are positive fuzzy numbers, that is to say, \(\forall a \in \left[ {0,1} \right],\underline {q\left( a \right)} r\underline {\left( a \right)} >0\) Google Scholar
  5. v.
    For the lower limit \(\mathop E\nolimits_l = \frac{{\underline {\mathop C\nolimits^* \left( a \right)} - \underline {C\left( a \right)} }}{{\underline {C\left( a \right)} }}\)and will be calculated for upper limits in a simila way.Google Scholar
  6. vi.
    Terceño, Márquez and Belvis (1997)Google Scholar
  7. vii.
    Not all methods for comparing fuzzy numbers are transitive, in the sense that the condition \(\mathop A\limits_ \sim >\mathop B\limits_ \sim\)and\(\mathop B\limits_ \sim >\mathop C\limits_ \sim\)may be fulfilled, and yet \(\mathop A\limits_ \sim >\mathop C\limits_ \sim\)may not be true. As we have said, this means it is not always possible to carry out either a complete comparison, or, consequently, a total ranking of all the fuzzy numbers in which we are interested.Google Scholar
  8. viii.
    Comparison of n fuzzy numbers requires n(n-1)/2 comparative operations, which presents operational problems if n is a high number.Google Scholar
  9. ix.
    Any comparison problem can be solved when taken as a ranking problem. llte opposite is not always true.Google Scholar
  10. x.
    In addition to those cited in the text, the most Widely-known methods in fuzzy literature may be found in Freeling (1980, 341–354), McCahon and Lee (1990, 159–181) and Kitainik (1993, 109–136), although this list does not pretend to be exhaustive.Google Scholar
  11. xi.
    As a translation of ‘indice de consentimiento’, usecl by Kaufmann and Gil (1987).Google Scholar
  12. xii.
    In some ways, the index of consent that we have presented is a method of ordering fuzzy numbers.Google Scholar
  13. xiii.
    We are aware that the NPV and IRR models for investment selection as presented represent another series of limitations (choice of the calculation and reference interest rates respectively, reinvesnnent of intermediate cash flows at the interest rate or at the IRR itself, effects of inflation and taxes, inconsistency of the IRR criterion, interaction between projects, interrelation between the investment projects and their financing, optimum time distribution of the investments, etc.) We will focus the chapter exclusively on the inconveniences specified.Google Scholar
  14. xiv.
    In the example, we got the same ranking for a*=0 as for a*=0,2 by all the ranking methods used. Thus the thre,e investment projects under consideration offer results that are easily differentiated. Clearly, it does not have to be that way, and will depend on the actual form of the membership functions of the fuzzy numbers to be ranked.Google Scholar
  15. xv.
    We take the triangular approximation of the result obtained, for its ease of operation and for the minimal error made in its calculation.Google Scholar
  16. xvi.
    It is generally accepted that the value of a company can be identified with the discounted value of future dividends which participation in the capital will offer. In this way, \(\sum\nolimits_{\forall i} {\mathop w\nolimits_i } \mathop D\nolimits_i\)can be understood as the increase in the company’s value which will result from the current investment progranune.Google Scholar
  17. xvii.
    \(\mathop A\limits_ \sim \leqslant {}_{a*}\mathop B\limits_ \sim\)in the strict sense if \(\overline {A\left( {\mathop a\nolimits^* } \right)} \leqslant \underline {B\left( {\mathop a\nolimits^* } \right)}\)However, this is not usually taken into consideration in PLP as it is an excessively restrictive criterion.Google Scholar


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • A. Terceño
  • J. de Andrés
  • M. G. Barberà
  • T. Lorenzana

There are no affiliations available

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