IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_5067.html
   My bibliography  Save this paper

Lattices and Lotteries in Apportioning Risk

Author

Listed:
  • Harris Schlesinger

Abstract

Although risk aversion has been used in economic models for over 275 years, the past few decades have shown how higher order risk attitudes are also quite important. A behavioral approach to defining such risk attitudes was developed by Eeckhoudt and Schlesinger (2006), based upon simple lottery preference. This article show how the mathematics of lattice theory can be used to model these lottery preferences. In addition to modeling a simple lattice structure, I show how such lattices can be extended in order to develop a better understanding of higher order risk attitudes.

Suggested Citation

  • Harris Schlesinger, 2014. "Lattices and Lotteries in Apportioning Risk," CESifo Working Paper Series 5067, CESifo.
    • Handle: RePEc:ces:ceswps:_5067
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp5067.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jokung, Octave, 2011. "Risk apportionment via bivariate stochastic dominance," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 448-452.
    2. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    3. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    4. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2013. "Even (Mixed) Risk Lovers Are Prudent," American Economic Review, American Economic Association, vol. 103(4), pages 1529-1535, June.
    5. Sebastian Ebert, 2013. "Even (Mixed) Risk Lovers Are Prudent: Comment," American Economic Review, American Economic Association, vol. 103(4), pages 1536-1537, June.
    6. Louis Eeckhoudt, 2012. "Beyond Risk Aversion: Why, How and What's Next?*," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(2), pages 141-155, September.
    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. Paan Jindapon & Liqun Liu & William S. Neilson, 2021. "Comparative risk apportionment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 91-112, April.
    2. Loubergé, Henri & Malevergne, Yannick & Rey, Béatrice, 2020. "New Results for additive and multiplicative risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 140-151.
    3. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    4. Peter, Richard & Hofmann, Annette, 2024. "Precautionary risk-reduction and saving decisions: Two sides of the same coin?," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 175-194.
    5. Sebastian Ebert & Daniel Wiesen, 2014. "Joint measurement of risk aversion, prudence, and temperance," Journal of Risk and Uncertainty, Springer, vol. 48(3), pages 231-252, June.
    6. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    7. Gollier, Christian, 2019. "Variance stochastic orders," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 1-8.
    8. 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.
    9. Xu, Guo & Wing-Keung, Wong & Lixing, Zhu, 2013. "Almost Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 51744, University Library of Munich, Germany.
    10. Irene Mussio & Maximiliano Sosa Andrés & Abdul H Kidwai, 2023. "Higher order risk attitudes in the time of COVID-19: an experimental study," Oxford Economic Papers, Oxford University Press, vol. 75(1), pages 163-182.
    11. Wang, Hongxia & Wang, Jianli & Li, Jingyuan & Xia, Xinping, 2015. "Precautionary paying for stochastic improvements under background risks," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 180-185.
    12. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    13. Denuit, Michel & Rey, Béatrice, 2013. "Another look at risk apportionment," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 335-343.
    14. Ruodu Wang & Qinyu Wu, 2024. "The reference interval in higher-order stochastic dominance," Papers 2411.15401, arXiv.org, revised Dec 2024.
    15. Heinzel Christoph & Richard Peter, 2021. "Precautionary motives with multiple instruments," Working Papers SMART 21-09, INRAE UMR SMART.
    16. Kanchan Joshi & Thiagu Ranganathan & Ram Ranjan, 2021. "Exploring Higher Order Risk Preferences of Farmers in a Water-Scarce Region: Evidence from a Field Experiment in West Bengal, India," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(2), pages 317-344, June.
    17. De Donno, Marzia & Menegatti, Mario, 2024. "Preferences on discounting under time risk," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    18. Haering, Alexander, 2021. "Framing decisions in experiments on higher-order risk preferences," Ruhr Economic Papers 913, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    19. Christophe Courbage & Béatrice Rey, 2020. "On temperance and risk spreading," Theory and Decision, Springer, vol. 88(4), pages 527-539, May.
    20. Sebastian Ebert & Diego C. Nocetti & Harris Schlesinger, 2018. "Greater Mutual Aggravation," Management Science, INFORMS, vol. 64(6), pages 2809-2811, June.

    More about this item

    Keywords

    risk apportionment; mixed risk aversion; mixed risk loving; lattice theory; submodular function;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:ces:ceswps:_5067. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    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.