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Risk Aversion for Investors with Memory: Hereditary Generalizations of Arrow-Pratt Measure

Author

Listed:
  • Valentina V. Tarasova

    (Lomonosov Moscow State University, Moscow 119991, Russia)

  • Vasily E. Tarasov

    (Lomonosov Moscow State University, Moscow 119991, Russia)

Abstract

The paper proposes a generalization of the Arrow-Pratt measures of absolute risk-aversion (ARA) for the case of financial processes with memory. The authors take into account the presence of the investors’memory in the description of their behavior. Standard risk aversion measures, which are defined by derivatives of integer orders, are actually based on the assumption of investors’ amnesia, because these derivatives are determined by the properties of the function only in an infinitesimal neighborhood of the point (point in time or amount of wealth). The authors propose a method that allows them to refuse the assumptions about absence of a memory about changes of the utility function and value of assets. In order to take into account the memory effects the authors used mathematical tools of derivatives (integro-differentiations) of non-integer orders. Formulas of hereditary generalizations.

Suggested Citation

  • Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Risk Aversion for Investors with Memory: Hereditary Generalizations of Arrow-Pratt Measure," Finansovyj žhurnal — Financial Journal, Financial Research Institute, Moscow 125375, Russia, issue 2, pages 46-63, April.
  • Handle: RePEc:fru:finjrn:170205:p:46-63
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    References listed on IDEAS

    as
    1. Bernanke, Ben & Gertler, Mark & Gilchrist, Simon, 1996. "The Financial Accelerator and the Flight to Quality," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 1-15, February.
    2. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    3. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
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    Citations

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    Cited by:

    1. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    2. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    3. Valentina V. Tarasova & Vasily E. Tarasov, 2017. "Concept of dynamic memory in economics," Papers 1712.09088, arXiv.org.

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    More about this item

    Keywords

    investment risks; risk of failure; risk aversion; Arrow-Pratt measure; utility function; investor behavior; memory effect; derivatives of non-integer order;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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