IDEAS home Printed from https://ideas.repec.org/a/bpj/apjrin/v11y2017i1p19n1.html
   My bibliography  Save this article

Bounded, Sigmoid Utility for Insurance Applications

Author

Listed:
  • Gao Siwei

    (Department of Accounting, Finance and Information Systems, Eastern Kentucky University, 521 Lancaster Ave., Richmond, KY 40475, United States of America)

  • Powers Michael R.

    (Finance Department, Tsinghua University, 386C Weilun Building, Beijing, Beijing 100084, China)

Abstract

Applying a well-known argument of Karl Menger to an insurance version of the St. Petersburg Paradox (in which the decision maker is confronted with losses, rather than gains), one can assert that von Neumann-Morgenstern utility functions are necessarily concave upward and bounded below as decision-maker wealth tends to negative infinity. However, this argument is subject to two potential criticisms: (1) infinite-mean losses do not exist in the real world; and (2) the St. Petersburg Paradox derives its force from empirical observation (i. e., that actual decision makers would not agree to an arbitrarily large insurance bid price to transfer an infinite-mean loss), and thus does not impart logical necessity. In the present article, these two criticisms are addressed in turn. We first show that, although infinite-mean insurance losses technically do not exist, they do provide a reasonable model for certain large (i. e., excess and reinsurance) property-liability indemnities. We then employ the Two-Envelope Paradox to demonstrate the logical necessity of concave-upward, lower-bounded utility for arbitrarily small (i. e., negative) values of wealth. Finally, we note that recognizing the bounded, sigmoid nature of utility functions challenges certain fundamental understandings in the economics of insurance demand, and can lead to vastly different conclusions regarding the bid price for insurance.

Suggested Citation

  • Gao Siwei & Powers Michael R., 2017. "Bounded, Sigmoid Utility for Insurance Applications," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 11(1), pages 1-19, January.
  • Handle: RePEc:bpj:apjrin:v:11:y:2017:i:1:p:19:n:1
    DOI: 10.1515/apjri-2016-0009
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/apjri-2016-0009
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/apjri-2016-0009?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. Ole Peters, 2011. "Menger 1934 revisited," Papers 1110.1578, arXiv.org.
    2. 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..
    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. Michael R. Powers & George Zanjani, 2013. "Insurance Risk, Risk Measures, and Capital Allocation: Navigating a Copernican Shift," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 201-223, November.
    5. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 117-137, May.
    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. Valerii Salov, 2015. "The Role of Time in Making Risky Decisions and the Function of Choice," Papers 1512.08792, arXiv.org.
    2. van den Bergh, J.C.J.M. & Botzen, W.J.W., 2015. "Monetary valuation of the social cost of CO2 emissions: A critical survey," Ecological Economics, Elsevier, vol. 114(C), pages 33-46.
    3. Shoji, Isao & Kanehiro, Sumei, 2016. "Disposition effect as a behavioral trading activity elicited by investors' different risk preferences," International Review of Financial Analysis, Elsevier, vol. 46(C), pages 104-112.
    4. Jonathan Meng & Feng Fu, 2020. "Understanding Gambling Behavior and Risk Attitudes Using Cryptocurrency-based Casino Blockchain Data," Papers 2008.05653, arXiv.org, revised Aug 2020.
    5. Daniel Fonseca Costa & Francisval Carvalho & Bruno César Moreira & José Willer Prado, 2017. "Bibliometric analysis on the association between behavioral finance and decision making with cognitive biases such as overconfidence, anchoring effect and confirmation bias," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1775-1799, June.
    6. Boone, Jan & Sadrieh, Abdolkarim & van Ours, Jan C., 2009. "Experiments on unemployment benefit sanctions and job search behavior," European Economic Review, Elsevier, vol. 53(8), pages 937-951, November.
    7. Castro, Luciano de & Galvao, Antonio F. & Kim, Jeong Yeol & Montes-Rojas, Gabriel & Olmo, Jose, 2022. "Experiments on portfolio selection: A comparison between quantile preferences and expected utility decision models," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 97(C).
    8. Jos'e Cl'audio do Nascimento, 2019. "Behavioral Biases and Nonadditive Dynamics in Risk Taking: An Experimental Investigation," Papers 1908.01709, arXiv.org, revised Apr 2023.
    9. Francesco GUALA, 2017. "Preferences: Neither Behavioural nor Mental," Departmental Working Papers 2017-05, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    10. Bin Zou, 2017. "Optimal Investment In Hedge Funds Under Loss Aversion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-32, May.
    11. Itzhak Gilboa & Andrew Postlewaite & Larry Samuelson & David Schmeidler, 2019. "What are axiomatizations good for?," Theory and Decision, Springer, vol. 86(3), pages 339-359, May.
    12. Wiafe, Osei K. & Basu, Anup K. & Chen, En Te, 2020. "Portfolio choice after retirement: Should self-annuitisation strategies hold more equities?," Economic Analysis and Policy, Elsevier, vol. 65(C), pages 241-255.
    13. Nicholas Barberis, 2012. "A Model of Casino Gambling," Management Science, INFORMS, vol. 58(1), pages 35-51, January.
    14. Lovric, M. & Kaymak, U. & Spronk, J., 2008. "A Conceptual Model of Investor Behavior," ERIM Report Series Research in Management ERS-2008-030-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    15. Goytom Abraha Kahsay & Daniel Osberghaus, 2018. "Storm Damage and Risk Preferences: Panel Evidence from Germany," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(1), pages 301-318, September.
    16. Carolin Bock & Maximilian Schmidt, 2015. "Should I stay, or should I go? – How fund dynamics influence venture capital exit decisions," Review of Financial Economics, John Wiley & Sons, vol. 27(1), pages 68-82, November.
    17. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2013. "Risk-averse and Risk-seeking Investor Preferences for Oil Spot and Futures," Documentos de Trabajo del ICAE 2013-31, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Aug 2013.
    18. Paredes-Frigolett, Harold, 2016. "Modeling the effect of responsible research and innovation in quadruple helix innovation systems," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 126-133.
    19. Karle, Heiko & Schumacher, Heiner & Vølund, Rune, 2023. "Consumer loss aversion and scale-dependent psychological switching costs," Games and Economic Behavior, Elsevier, vol. 138(C), pages 214-237.
    20. Christian Gollier & James Hammitt & Nicolas Treich, 2013. "Risk and choice: A research saga," Journal of Risk and Uncertainty, Springer, vol. 47(2), pages 129-145, October.

    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:bpj:apjrin:v:11:y:2017:i:1:p:19:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.