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How to Calibrate a Questionnaire for Risk Measurement?

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 643))

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Abstract

Utility functions content parameters related to risk aversion coefficients which represent natural extensions of utility function properties. They measure how much utility we gain (or lose) as we add (or subtract) from our wealth. We set up these parameters for a person based on her/his answers to a questionnaire constructed to identify individual risk behavior. Calibration of such a questionnaire, and subsequently of utility functions, is based on an expected utility maximization of different alternatives of investment strategies. In the paper, we present questionnaire calibration methodology which we illustrate using absolute and relative risk aversion coefficients of two selected utility functions which have common, as well as different properties.

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Notes

  1. 1.

    Percentage of possible profit or loss sequentially in all alternatives.

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Acknowledgement

Jana Špirková has been supported by the Project VEGA no. 1/0093/17 Identification of risk factors and their impact on products of the insurance and savings schemes.

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Authors and Affiliations

  1. Faculty of Economics, Matej Bel University, Banská Bystrica, Slovakia

    Jana Špirková & Pavol Král’

Authors
  1. Jana Špirková
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  2. Pavol Král’
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Corresponding author

Correspondence to Jana Špirková .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Institute of Biophysics and Biomedical Engineering, Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

Appendix

All computations were made with fundamental investments divided by 10,000.

Appendix

Table 2. Expected utilities according to power utility function (7) with \(p=0.8\) and \(w=17{,}000\) €
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Table 3. Maximal expected utilities for power utility function (7) of the alternative \(A_{4}\)
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Table 4. Maximal expected utilities for power utility function (7) of the alternative \(A_{3}\)
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Table 5. Expected utilities evaluated by the exponential utility function (10) with \(p=0.8\), \(w=17{,}000\) €
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Table 6. Expected utilities evaluated by the exponential utility function (10) with \(p=0.8\), \(w=13{,}500\) €
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Table 7. Maximal expected utilities and corresponding \(\alpha \) for exponential utility function (10) of the alternative \(A_{3}\)
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Table 8. Maximal premium for \(A_{4}\) according to (7), \(p=0.8\), \(w=17{,}000\) €
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Table 9. Maximal premium for \(A_{4}\) according to (10), \(p=0.8\), \(w=17{,}000\) €, and \(w=13{,}500\) €
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Špirková, J., Král’, P. (2018). How to Calibrate a Questionnaire for Risk Measurement?. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 643. Springer, Cham. https://doi.org/10.1007/978-3-319-66827-7_32

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  • DOI: https://doi.org/10.1007/978-3-319-66827-7_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

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