IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v72y2017icp70-81.html
   My bibliography  Save this article

How risky is a random process?

Author

Listed:
  • Shah, Sudhir A.

Abstract

The riskiness of random processes is compared by (a) employing a decision theoretic equivalence between processes and lotteries on path-spaces to identify the riskiness of the former with that of the latter, and (b) using the theory of comparative riskiness of lotteries over vector spaces to compare the riskiness of lotteries on a given path-space. We derive the equivalence used in step (a) and contribute a new criterion to the theory applied in step (b). The validity of the new criterion, which applies second order stochastic dominance to utility distributions, is established by showing its equivalence to the benchmark decision theoretic criterion when comparing the riskiness of lotteries over any vector space. We demonstrate the theory’s tractability via diverse economic applications.

Suggested Citation

  • Shah, Sudhir A., 2017. "How risky is a random process?," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 70-81.
    • Handle: RePEc:eee:mateco:v:72:y:2017:i:c:p:70-81
    DOI: 10.1016/j.jmateco.2017.06.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406817300885
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2017.06.005?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. Diamond, Peter A. & Stiglitz, Joseph E., 1974. "Increases in risk and in risk aversion," Journal of Economic Theory, Elsevier, vol. 8(3), pages 337-360, July.
    2. Perlman, Michael D., 1974. "Jensen's inequality for a convex vector-valued function on an infinite-dimensional space," Journal of Multivariate Analysis, Elsevier, vol. 4(1), pages 52-65, March.
    3. Susan Athey, 2002. "Monotone Comparative Statics under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(1), pages 187-223.
    4. William R. Russell & Tae Kun Seo, 1978. "Ordering Uncertain Prospects: The Multivariate Utility Functions Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 605-610.
    5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    6. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    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. Stelios Arvanitis, 2021. "Stochastic dominance efficient sets and stochastic spanning," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 401-409, June.
    2. Wang, Huiqi & Yuan, Wei & Yuan, George, 2022. "The mechanism for SMEs growth by applying stochastic dynamical approach," Finance Research Letters, Elsevier, vol. 48(C).

    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. Sudhir A. Shah, 2010. "Comparative Riskiness Of Random Vector Outcomes," Working papers 191, Centre for Development Economics, Delhi School of Economics.
    2. Drewianka, Scott, 2006. "A generalized model of commitment," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 233-251, December.
    3. Andrés Fioriti & Allan Hernandez-Chanto, 2022. "Leveling the Playing Field for Risk-Averse Agents in Security-Bid Auctions," Management Science, INFORMS, vol. 68(7), pages 5441-5463, July.
    4. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
    5. Mark Huggett, 2004. "Precautionary Wealth Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 769-781.
    6. Chateauneuf, A. & Lakhnati, G., 2015. "Increases in risk and demand for a risky asset," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 44-48.
    7. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, vol. 57(8), pages 1406-1423, August.
    8. Grant, S. & Quiggin, J., 2001. "A Model-Free Definition of Increasing Uncertainty," Discussion Paper 2001-84, Tilburg University, Center for Economic Research.
    9. Arthur Charpentier & Alfred Galichon & Marc Henry, 2012. "Local Utility and Multivariate Risk Aversion," CIRJE F-Series CIRJE-F-836, CIRJE, Faculty of Economics, University of Tokyo.
    10. Quiggin, John & Chambers, Robert G., 2006. "Supermodularity and risk aversion," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 1-14, July.
    11. 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.
    12. Donald C. Keenan & Arthur Snow, 2016. "Strong Increases in Downside Risk Aversion," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 41(2), pages 149-161, September.
    13. Broll, Udo & Wong, Keith K.P., 2010. "The firm under uncertainty: capital structure and background risk," Dresden Discussion Paper Series in Economics 04/10, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    14. Gollier, Christian & Schlesinger, Harris, 2002. "Changes in risk and asset prices," Journal of Monetary Economics, Elsevier, vol. 49(4), pages 747-760, May.
    15. Muller, Alfred, 1998. "Comparing risks with unbounded distributions," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 229-239, September.
    16. Gatti, J. Rupert J., 1999. "Multi-Commodity Consumer Search," Journal of Economic Theory, Elsevier, vol. 86(2), pages 219-244, June.
    17. Aflaki, Sam, 2013. "The effect of environmental uncertainty on the tragedy of the commons," Games and Economic Behavior, Elsevier, vol. 82(C), pages 240-253.
    18. Justin P. Johnson & David P. Myatt, 2006. "On the Simple Economics of Advertising, Marketing, and Product Design," American Economic Review, American Economic Association, vol. 96(3), pages 756-784, June.
    19. Chen, Kevin & Meilke, Karl & Turvey, Calum, 1996. "Theory of Prudent Farm Households and Agricultural Insurance," Working Papers 244799, University of Guelph, Department of Food, Agricultural and Resource Economics.
    20. Jordi Caballe & Joan Esteban, 2007. "Stochastic Dominance and Absolute Risk Aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 89-110, January.

    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:mateco:v:72:y:2017:i:c:p:70-81. 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/jmateco .

    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.