IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v61y2023i4d10.1007_s10614-022-10252-8.html
   My bibliography  Save this article

The Slicing Method: Determining Insensitivity Regions of Probability Weighting Functions

Author

Listed:
  • Martín Egozcue

    (University of Montevideo
    Catholic University of Uruguay
    Norte Construcciones S.A.)

  • Luis Fuentes García

    (Universidade da Coruña)

  • Ričardas Zitikis

    (Western University
    York University)

Abstract

A popular rule of thumb, usually called “heuristic technique” in Behavioral Economics, for determining the likelihood insensitivity regions of probability weighting functions (pwf’s) is based on searching for points at which the pwf’s are twice their values at half the points. Although this technique works remarkably well for many commonly used pwf’s, it sometimes fails to provide the correct answer. In order to cover the class of pwf’s for which the heuristic technique does not work, in this paper we propose, discuss, and illustrate an extension of the technique into what we call the “slicing method,” which is capable of finding the subadditivity and insensitivity regions of any continuous pwf.

Suggested Citation

  • Martín Egozcue & Luis Fuentes García & Ričardas Zitikis, 2023. "The Slicing Method: Determining Insensitivity Regions of Probability Weighting Functions," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1369-1402, April.
    • Handle: RePEc:kap:compec:v:61:y:2023:i:4:d:10.1007_s10614-022-10252-8
    DOI: 10.1007/s10614-022-10252-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-022-10252-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-022-10252-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Walther, Herbert, 2003. "Normal-randomness expected utility, time preference and emotional distortions," Journal of Economic Behavior & Organization, Elsevier, vol. 52(2), pages 253-266, October.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
    6. Ali al-Nowaihi & Sanjit Dhami, 2010. "Probability Weighting Functions," Discussion Papers in Economics 10/10, Division of Economics, School of Business, University of Leicester.
    7. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
    8. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    9. Helga Fehr-Duda & Thomas Epper, 2012. "Probability and Risk: Foundations and Economic Implications of Probability-Dependent Risk Preferences," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 567-593, July.
    10. Dhami, Sanjit, 2016. "The Foundations of Behavioral Economic Analysis," OUP Catalogue, Oxford University Press, number 9780198715535.
    11. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    12. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    13. Doering, Jana & Kizys, Renatas & Juan, Angel A. & Fitó, Àngels & Polat, Onur, 2019. "Metaheuristics for rich portfolio optimisation and risk management: Current state and future trends," Operations Research Perspectives, Elsevier, vol. 6(C).
    14. Chao Gong & Chunhui Xu & Ji Wang, 2018. "An Efficient Adaptive Real Coded Genetic Algorithm to Solve the Portfolio Choice Problem Under Cumulative Prospect Theory," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 227-252, June.
    15. Marie Pfiffelmann, 2011. "Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting," Theory and Decision, Springer, vol. 71(3), pages 325-341, September.
    16. David Picken & Ben Ilozor, 2003. "Height and construction costs of buildings in Hong Kong," Construction Management and Economics, Taylor & Francis Journals, vol. 21(2), pages 107-111.
    17. Edward Furman & Ričardas Zitikis, 2009. "Weighted Pricing Functionals With Applications to Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(4), pages 483-496.
    18. Marc Rieger & Mei Wang, 2006. "Cumulative prospect theory and the St. Petersburg paradox," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 665-679, August.
    19. Izhakian, Yehuda, 2020. "A theoretical foundation of ambiguity measurement," Journal of Economic Theory, Elsevier, vol. 187(C).
    20. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    21. Stephen G. Dimmock & Roy Kouwenberg & Peter P. Wakker, 2016. "Ambiguity Attitudes in a Large Representative Sample," Management Science, INFORMS, vol. 62(5), pages 1363-1380, May.
    22. Barr, Jason M., 2016. "Building the Skyline: The Birth and Growth of Manhattan's Skyscrapers," OUP Catalogue, Oxford University Press, number 9780199344369.
    23. Neilson, William S & Stowe, Jill, 2002. "A Further Examination of Cumulative Prospect Theory Parameterizations," Journal of Risk and Uncertainty, Springer, vol. 24(1), pages 31-46, January.
    24. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    25. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    26. Michael Best & Robert Grauer & Jaroslava Hlouskova & Xili Zhang, 2014. "Loss-Aversion with Kinked Linear Utility Functions," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 45-65, June.
    27. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    28. Sunstein, Cass R, 2003. "Terrorism and Probability Neglect," Journal of Risk and Uncertainty, Springer, vol. 26(2-3), pages 121-136, March-May.
    29. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
    30. Enrico Giorgi & Thorsten Hens & János Mayer, 2007. "Computational aspects of prospect theory with asset pricing applications," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 267-281, May.
    31. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    2. Martina Nardon & Paolo Pianca, 2019. "Behavioral premium principles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 229-257, June.
    3. Arjan Verschoor & Ben D’Exelle, 2022. "Probability weighting for losses and for gains among smallholder farmers in Uganda," Theory and Decision, Springer, vol. 92(1), pages 223-258, February.
    4. Eyal Baharad & Doron Kliger, 2013. "Market failure in light of non-expected utility," Theory and Decision, Springer, vol. 75(4), pages 599-619, October.
    5. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.
    6. Thomas Epper & Helga Fehr-Duda, 2012. "The missing link: unifying risk taking and time discounting," ECON - Working Papers 096, Department of Economics - University of Zurich, revised Oct 2018.
    7. Ilke Aydogan & Yu Gao, 2020. "Experience and rationality under risk: re-examining the impact of sampling experience," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1100-1128, December.
    8. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    9. Víctor González-Jiménez, 2021. "Incentive contracts when agents distort probabilities," Vienna Economics Papers vie2101, University of Vienna, Department of Economics.
    10. Kpegli, Yao Thibaut & Corgnet, Brice & Zylbersztejn, Adam, 2023. "All at once! A comprehensive and tractable semi-parametric method to elicit prospect theory components," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    11. Özalp Özer & Yanchong Zheng, 2016. "Markdown or Everyday Low Price? The Role of Behavioral Motives," Management Science, INFORMS, vol. 62(2), pages 326-346, February.
    12. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    13. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    14. Ferdinand M. Vieider & Clara Villegas-Palacio & Peter Martinsson & Milagros Mejía, 2016. "Risk Taking For Oneself And Others: A Structural Model Approach," Economic Inquiry, Western Economic Association International, vol. 54(2), pages 879-894, April.
    15. Pavlo R. Blavatskyy, 2005. "Back to the St. Petersburg Paradox?," Management Science, INFORMS, vol. 51(4), pages 677-678, April.
    16. Víctor González-Jiménez, 2021. "Incentive contracts when agents distort probabilities," Vienna Economics Papers 2101, University of Vienna, Department of Economics.
    17. Marie Pfiffelmann, 2011. "Solving the St. Petersburg Paradox in cumulative prospect theory: the right amount of probability weighting," Theory and Decision, Springer, vol. 71(3), pages 325-341, September.
    18. Dierkes, Maik & Germer, Stephan & Sejdiu, Vulnet, 2020. "Probability distortion, asset prices, and economic growth," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 84(C).
    19. Martina Nardon & Paolo Pianca, 2019. "European option pricing under cumulative prospect theory with constant relative sensitivity probability weighting functions," Computational Management Science, Springer, vol. 16(1), pages 249-274, February.
    20. Francesco Cesarone & Massimiliano Corradini & Lorenzo Lampariello & Jessica Riccioni, 2023. "A new behavioral model for portfolio selection using the Half-Full/Half-Empty approach," Papers 2312.10749, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:61:y:2023:i:4:d:10.1007_s10614-022-10252-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.