IDEAS home Printed from https://ideas.repec.org/a/the/publsh/1499.html
   My bibliography  Save this article

The Foster-Hart measure of riskiness for general gambles

Author

Listed:
  • Hellmann, Tobias

    () (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    () (Center for Mathematical Economics, Bielefeld University)

Abstract

Foster and Hart propose a measure of riskiness for discrete random variables. Their defining equation has no solution for many common continuous distributions. We show how to extend consistently the definition of riskiness to continuous random variables. For many continuous random variables, the risk measure is equal to the worst--case risk measure, i.e. the maximal possible loss incurred by that gamble. For many discrete gambles with a large number of values, the Foster--Hart riskiness is close to the maximal loss. We give a simple characterization of gambles whose riskiness is or is close to the maximal loss.

Suggested Citation

  • Hellmann, Tobias & Riedel, Frank, 2015. "The Foster-Hart measure of riskiness for general gambles," Theoretical Economics, Econometric Society, vol. 10(1), January.
  • Handle: RePEc:the:publsh:1499
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20150001/12309/363
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert J. Aumann & Roberto Serrano, 2008. "An Economic Index of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 116(5), pages 810-836, October.
    2. Hellmann, Tobias & Riedel, Frank, 2015. "A dynamic extension of the Foster–Hart measure of riskiness," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 66-70.
    3. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, vol. 57(8), pages 1406-1423, August.
    4. Dean P. Foster & Sergiu Hart, 2009. "An Operational Measure of Riskiness," Journal of Political Economy, University of Chicago Press, vol. 117(5), pages 785-814.
    5. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    6. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Hart, Sergiu & Foster, Dean P., 2013. "A wealth-requirement axiomatization of riskiness," Theoretical Economics, Econometric Society.
    9. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    10. Homm, Ulrich & Pigorsch, Christian, 2012. "An operational interpretation and existence of the Aumann–Serrano index of riskiness," Economics Letters, Elsevier, vol. 114(3), pages 265-267.
    11. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    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. Ehsani, Sina & Lien, Donald, 2015. "A note on minimum riskiness hedge ratio," Finance Research Letters, Elsevier, vol. 15(C), pages 11-17.
    2. Chamorro Elosua, Arritokieta & Usategui Díaz de Otalora, José María, 2013. "A Note on Risk Acceptance, Bankruptcy Avoidance and Riskiness Measures," DFAEII Working Papers DFAEII;2013-04, University of the Basque Country - Department of Foundations of Economic Analysis II.
    3. Hellmann, Tobias & Riedel, Frank, 2015. "A dynamic extension of the Foster–Hart measure of riskiness," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 66-70.
    4. Anand, Abhinav & Li, Tiantian & Kurosaki, Tetsuo & Kim, Young Shin, 2016. "Foster–Hart optimal portfolios," Journal of Banking & Finance, Elsevier, vol. 68(C), pages 117-130.
    5. repec:eee:ecolet:v:159:y:2017:i:c:p:149-152 is not listed on IDEAS

    More about this item

    Keywords

    Risk measures; operational; bankruptcy; continuous random variable;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    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:the:publsh:1499. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Martin J. Osborne). General contact details of provider: http://econtheory.org .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.