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Mathematical Methods for Making Investment Decisions

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Mathematical Methods and Models in Economic Planning, Management and Budgeting

Abstract

Investment to the development of economic processes and systems always entails risks. Not adequately reasoned investment decision can cause adverse economic consequences for the investor. Making investment decisions becomes more complicated because of high degree of uncertainty of economic consequences of investments. Mathematical methods and models proposed in the chapter represent an integrated methodology of making investment decisions that enables to reduce risks, more objectively estimate probability of investment consequences and equip the investor with a practical instrument of scientifically-based forecasting. A review of a variety of methodological approaches to risk studying shows that researchers mainly focus their attention on the entrepreneurial risk, i.e. as the object of analysis they consider individual enterprises, and the subjects of their investigations are statistical variations in stochastic probability distributions of all possible losses and damages. At the same time, insufficient attention is given to the investigation of principles of functioning and forms of manifestation of nonstatistical risks, their influence on the entrepreneurial activity and interaction with statistical risks. This research suggests a methodological base for creation of an integral expert system supporting coordinated investment decisions with account for assessment and control of project risks.

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Notes

  1. 1.

    Instability in the IP external environment, as a rule, means fluctuations r i (ρ).

  2. 2.

    Remark: Not obligatory “probability.”

  3. 3.

    The boundaries of the stability zone are defined on the basis of the accepted requirements for investment efficiency.

  4. 4.

    The decision can be predicted with satisfactory accuracy on the assumption of sufficient stability, inertia, etc.

  5. 5.

    This means not only computing difficulties (modern information technologies smooth over this problem), but also psychological difficulties related to the level of experts’ professionalism.

  6. 6.

    One can make a comparative analysis of precision of estimates obtained by the first and second methods.

  7. 7.

    Proved in the theory of matrix algebra.

  8. 8.

    Here [⋅]—the integer part of number (⋅).

  9. 9.

    It is supposed that if π(a)>π(b)⇔a is better than b.

  10. 10.

    Normalization may be required to obtain a unit sum of weights.

  11. 11.

    It is convenient to use the same notations for the criterion and its numerous values, since it will cause no misunderstandings in the context.

  12. 12.

    Qualitatively, this means “higher.”

  13. 13.

    The existence of correlated variables in the project analysis can lead to incorrect results: computer iterations are a completely computerized part of the project risk analysis, therefore in considering key variables to be independent one can generate unrealistic project scenarios. For example, if there are two negatively correlated variables, say price and sales volume, and if their correlation coefficient is not exactly defined, there can be scenarios randomly generated by the computer where both variables are either high or low, which will negatively affect the result.

  14. 14.

    The classical criterion is W=0. However, based on the strategic plans W can take any value, even negative: if the project diversifies the investor’s activities and improves reliability of his business or the investor consciously takes an increased risk for the sake of increase in the weighted average capital return, the marginal project is accepted.

  15. 15.

    The choice of this indicator for illustration of some situations is explained by its popularity.

  16. 16.

    The exchange rate is taken for the moment of work execution.

  17. 17.

    In this case the sampling is too small to make a conclusion based on expected values.

  18. 18.

    A numerical value of the linguistic variable.

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  1. Al-Farabi Kazakh National University, Almaty, Kazakhstan

    Galimkair Mutanov

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Mutanov, G. (2015). Mathematical Methods for Making Investment Decisions. In: Mathematical Methods and Models in Economic Planning, Management and Budgeting. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45142-7_6

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