IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v50y2012i1p159-166.html
   My bibliography  Save this article

Pricing insurance contracts under Cumulative Prospect Theory

Author

Listed:
  • Kaluszka, Marek
  • Krzeszowiec, Michał

Abstract

The aim of this paper is to introduce a premium principle which relies on Cumulative Prospect Theory by Kahneman and Tversky. Some special cases of this premium principle have already been studied in the actuarial literature. In the paper, properties of this premium principle are examined.

Suggested Citation

  • Kaluszka, Marek & Krzeszowiec, Michał, 2012. "Pricing insurance contracts under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 159-166.
  • Handle: RePEc:eee:insuma:v:50:y:2012:i:1:p:159-166
    DOI: 10.1016/j.insmatheco.2011.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711001223
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.insmatheco.2011.11.001?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. Ulrich Schmidt & Horst Zank, 2007. "Linear cumulative prospect theory with applications to portfolio selection and insurance demand," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 30(1), pages 1-18, May.
    2. Ulrich Schmidt & Chris Starmer & Robert Sugden, 2008. "Third-generation prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 203-223, June.
    3. 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.
    4. Heilpern, S., 2003. "A rank-dependent generalization of zero utility principle," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 67-73, August.
    5. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A. & Tang, Qihe, 2004. "A comonotonic image of independence for additive risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 581-594, December.
    6. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    7. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    8. van der Hoek, John & Sherris, Michael, 2001. "A class of non-expected utility risk measures and implications for asset allocations," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 69-82, February.
    9. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    10. Joshua C. Teitelbaum, 2007. "A Unilateral Accident Model under Ambiguity," The Journal of Legal Studies, University of Chicago Press, vol. 36(2), pages 431-477, June.
    11. Marek Kaluszka & Andrzej Okolewski, 2008. "An Extension of Arrow's Result on Optimal Reinsurance Contract," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 275-288, June.
    12. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, January.
    13. Tsanakas, Andreas, 2009. "To split or not to split: Capital allocation with convex risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 268-277, April.
    14. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    15. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    16. Botond Koszegi & Matthew Rabin, 2007. "Reference-Dependent Risk Attitudes," American Economic Review, American Economic Association, vol. 97(4), pages 1047-1073, September.
    17. Gerber, Hans U., 1985. "On additive principles of zero utility," Insurance: Mathematics and Economics, Elsevier, vol. 4(4), pages 249-251, October.
    18. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "A note on additive risk measures in rank-dependent utility," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 187-189, October.
    19. Shaun, Wang, 1995. "Insurance pricing and increased limits ratemaking by proportional hazards transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(1), pages 43-54, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Martina Nardon & Paolo Pianca, 2019. "Insurance premium calculation under continuous cumulative prospect theory," Working Papers 2019:03, Department of Economics, University of Venice "Ca' Foscari".
    2. Belles-Sampera, Jaume & Merigó, José M. & Guillén, Montserrat & Santolino, Miguel, 2013. "The connection between distortion risk measures and ordered weighted averaging operators," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 411-420.
    3. Kaluszka, Marek & Krzeszowiec, Michał, 2013. "On iterative premium calculation principles under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 435-440.
    4. Joanna Dębicka & Stanisław Heilpern, 2018. "Valuation and optimization of contracts on the secondary insurance market," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 51, pages 37-62.
    5. Chudziak, J., 2018. "On existence and uniqueness of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 243-246.
    6. Mao, Tiantian & Stupfler, Gilles & Yang, Fan, 2023. "Asymptotic properties of generalized shortfall risk measures for heavy-tailed risks," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 173-192.
    7. Joanna Dębicka & Stanisław Heilpern, 2020. "The optimization of insurance contracts on the viatical market," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(2), pages 5-27.
    8. 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.
    9. Bai, Chunguang & Sarkis, Joseph, 2017. "Improving green flexibility through advanced manufacturing technology investment: Modeling the decision process," International Journal of Production Economics, Elsevier, vol. 188(C), pages 86-104.
    10. Christian Biener & Martin Eling, 2013. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2012 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(2), pages 219-231, September.
    11. Kaluszka, M. & Laeven, R.J.A. & Okolewski, A., 2012. "A note on weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 379-381.
    12. Chudziak, J., 2020. "On positive homogeneity and comonotonic additivity of the principle of equivalent utility under Cumulative Prospect Theory," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 154-159.
    13. Tiantian Mao & Jun Cai, 2018. "Risk measures based on behavioural economics theory," Finance and Stochastics, Springer, vol. 22(2), pages 367-393, April.
    14. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    15. Sainan Zhang & Huifu Xu, 2022. "Insurance premium-based shortfall risk measure induced by cumulative prospect theory," Computational Management Science, Springer, vol. 19(4), pages 703-738, October.
    16. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    17. Marek Kałuszka & Michał Krzeszowiec, 2013. "Iteracyjność składek ubezpieczeniowych w ujęciu teorii skumulowanej perspektywy i teorii nieokreśloności," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 31, pages 45-56.

    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. 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.
    2. Martina Nardon & Paolo Pianca, 2019. "Insurance premium calculation under continuous cumulative prospect theory," Working Papers 2019:03, Department of Economics, University of Venice "Ca' Foscari".
    3. Katarzyna M. Werner & Horst Zank, 2019. "A revealed reference point for prospect theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 731-773, June.
    4. Choo, Weihao & de Jong, Piet, 2015. "The tradeoff insurance premium as a two-sided generalisation of the distortion premium," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 238-246.
    5. repec:cup:judgdm:v:16:y:2021:i:6:p:1324-1369 is not listed on IDEAS
    6. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    7. Aurélien Baillon & Han Bleichrodt & Vitalie Spinu, 2020. "Searching for the Reference Point," Management Science, INFORMS, vol. 66(1), pages 93-112, January.
    8. Dhami, Sanjit & al-Nowaihi, Ali, 2013. "An extension of the Becker proposition to non-expected utility theory," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 10-20.
    9. Sudeep Bhatia & Graham Loomes & Daniel Read, 2021. "Establishing the laws of preferential choice behavior," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 16(6), pages 1324-1369, November.
    10. Horst Zank, 2010. "On probabilities and loss aversion," Theory and Decision, Springer, vol. 68(3), pages 243-261, March.
    11. Johannes G. Jaspersen & Richard Peter & Marc A. Ragin, 2023. "Probability weighting and insurance demand in a unified framework," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 48(1), pages 63-109, March.
    12. Martina Nardon & Paolo Pianca, 2014. "European option pricing with constant relative sensitivity probability weighting function," Working Papers 2014:25, Department of Economics, University of Venice "Ca' Foscari".
    13. Vieider, Ferdinand M. & Truong, Nghi & Martinsson, Peter & Pham Khanh Nam & Martinsson, Peter, 2013. "Risk preferences and development revisited: A field experiment in Vietnam," Discussion Papers, WZB Junior Research Group Risk and Development SP II 2013-403, WZB Berlin Social Science Center.
    14. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    15. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2013. "Salience and Consumer Choice," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 803-843.
    16. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    17. Serge Blondel & Louis Lévy-garboua, 2011. "Can non-expected utility theories explain the paradox of not voting?," Economics Bulletin, AccessEcon, vol. 31(4), pages 3158-3168.
    18. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    19. 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.
    20. Dorian Jullien, 2018. "Under Risk, Over Time, Regarding Other People: Language and Rationality within Three Dimensions," Research in the History of Economic Thought and Methodology, in: Including a Symposium on Latin American Monetary Thought: Two Centuries in Search of Originality, volume 36, pages 119-155, Emerald Group Publishing Limited.
    21. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet E., 2010. "Behavioral econometrics for psychologists," Journal of Economic Psychology, Elsevier, vol. 31(4), pages 553-576, August.

    More about this item

    Keywords

    Cumulative Prospect Theory; Premium principle; Non-expected utility;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    Statistics

    Access and download statistics

    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:eee:insuma:v:50:y:2012:i:1:p:159-166. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.