IDEAS home Printed from https://ideas.repec.org/a/cup/astinb/v36y2006i01p219-243_01.html
   My bibliography  Save this article

Risk Exchange with Distorted Probabilities

Author

Listed:
  • Tsanakas, Andreas
  • Christofides, Nicos

Abstract

An exchange economy is considered, where agents (insurers/banks) trade risks. Decision making takes place under distorted probabilities, which are used to represent either rank-dependence of preferences or ambiguity with respect to real-world probabilities. Pricing formulas and risk allocations, generalising the results of Bühlmann (1980, 1984) are obtained via the construction of aggregate preferences from heterogeneous agents’ utility and distortion functions. This involves the introduction of a novel ‘collective ambiguity aversion’ coefficient. It is shown that probability distortion changes insurers’ behaviour, who trade not only to share the aggregate market risk, but are also found to bet against each other. Moreover, probability distortion tends to increase the price of insurance (increase asset returns). While the cases of rank-dependence and ambiguity are formally similar, an important distinction emerges as for rank-dependent preferences equilibria are determinate, while for ambiguity they are generally indeterminate.

Suggested Citation

  • Tsanakas, Andreas & Christofides, Nicos, 2006. "Risk Exchange with Distorted Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 219-243, May.
    • Handle: RePEc:cup:astinb:v:36:y:2006:i:01:p:219-243_01
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S051503610001446X/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Boonen, Tim J. & Jiang, Wenjun, 2022. "Bilateral risk sharing in a comonotone market with rank-dependent utilities," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 361-378.
    2. Aloisio Araujo, 2015. "General equilibrium, preferences and financial institutions after the crisis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 217-254, February.
    3. Choo, Weihao & de Jong, Piet, 2016. "Insights to systematic risk and diversification across a joint probability distribution," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 142-150.
    4. Robert, Christian Y. & Therond, Pierre-E., 2014. "Distortion Risk Measures, Ambiguity Aversion And Optimal Effort," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 277-302, May.
    5. Claire Mouminoux & Christophe Dutang & Stéphane Loisel & Hansjoerg Albrecher, 2022. "On a Markovian Game Model for Competitive Insurance Pricing," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1061-1091, June.
    6. repec:hal:wpaper:hal-00813199 is not listed on IDEAS
    7. Boonen, Tim J. & Pantelous, Athanasios A. & Wu, Renchao, 2018. "Non-cooperative dynamic games for general insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 123-135.
    8. Mario Ghossoub & Qinghua Ren & Ruodu Wang, 2024. "Counter-monotonic Risk Sharing with Heterogeneous Distortion Risk Measures," Papers 2412.00655, arXiv.org.
    9. Wüthrich Mario V. & Embrechts Paul & Tsanakas Andreas, 2011. "Risk margin for a non-life insurance run-off," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 299-317, December.
    10. 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.
    11. Masaaki Kijima & Akihisa Tamura, 2014. "Buhlmann’s Economic Premium Principle in The Presence of Transaction Costs," KIER Working Papers 893, Kyoto University, Institute of Economic Research.
    12. Tim J. Boonen & Fangda Liu & Ruodu Wang, 2021. "Competitive equilibria in a comonotone market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1217-1255, November.
    13. Mario Ghossoub & Qinghua Ren & Ruodu Wang, 2024. "Counter-monotonic risk allocations and distortion risk measures," Papers 2407.16099, arXiv.org.
    14. Araujo A. & Chateauneuf A. & Gama-Torres J. & Novinski R., 2014. "General equilibrium, risk taking and volatility," Working Papers 2014-181, Department of Research, Ipag Business School.
    15. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.

    More about this item

    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:cup:astinb:v:36:y:2006:i:01:p:219-243_01. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/asb .

    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.