IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v86y2020icp69-82.html

Increasing risk: Dynamic mean-preserving spreads

Author

Listed:
  • Arcand, Jean-Louis
  • Hongler, Max-Olivier
  • Rinaldo, Daniele

Abstract

We extend the celebrated Rothschild and Stiglitz (1970) definition of Mean-Preserving Spreads to a dynamic framework. We adapt the original integral conditions to transition probability densities, and give sufficient conditions for their satisfaction. We then focus on a class of nonlinear scalar diffusion processes, the super-diffusive ballistic process, and prove that it satisfies the integral conditions. We further prove that this class is unique among Brownian bridges. This class of processes can be generated by a random superposition of linear Markov processes with constant drifts. This exceptionally simple representation enables us to systematically revisit, by means of the properties of dynamic mean-preserving spreads, workhorse economic models originally based on White Gaussian Noise. A selection of four examples is presented and explicitly solved.

Suggested Citation

  • Arcand, Jean-Louis & Hongler, Max-Olivier & Rinaldo, Daniele, 2020. "Increasing risk: Dynamic mean-preserving spreads," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 69-82.
    • Handle: RePEc:eee:mateco:v:86:y:2020:i:c:p:69-82
    DOI: 10.1016/j.jmateco.2018.11.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406818301332
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2018.11.003?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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Rothschild, Michael & Stiglitz, Joseph E., 1972. "Addendum to "increasing risk: I. A definition"," Journal of Economic Theory, Elsevier, vol. 5(2), pages 306-306, October.
    3. Abel, Andrew B & Eberly, Janice C, 1994. "A Unified Model of Investment under Uncertainty," American Economic Review, American Economic Association, vol. 84(5), pages 1369-1384, December.
    4. 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.
    5. Yoram Halevy, 2015. "Time Consistency: Stationarity and Time Invariance," Econometrica, Econometric Society, vol. 83, pages 335-352, January.
    6. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Thou shalt buy and hold," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 765-776.
    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    8. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    9. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    10. Albert Shiryaev & Zuoquan Xu & Xun Yu Zhou, 2008. "Response to comment on 'Thou shalt buy and hold'," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 761-762.
    11. Machina, Mark J & Pratt, John W, 1997. "Increasing Risk: Some Direct Constructions," Journal of Risk and Uncertainty, Springer, vol. 14(2), pages 103-127, March.
    12. Abel, Andrew B, 1983. "Optimal Investment under Uncertainty," American Economic Review, American Economic Association, vol. 73(1), pages 228-233, March.
    13. Hongler, Max-Olivier & Filliger, Roger & Blanchard, Philippe, 2006. "Soluble models for dynamics driven by a super-diffusive noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 301-315.
    14. Jacques du Toit & Goran Peskir, 2009. "Selling a stock at the ultimate maximum," Papers 0908.1014, arXiv.org.
    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. Arcand, Jean-Louis & Kumar, Shekhar Hari & Hongler, Max-Olivier & Rinaldo, Daniele, 2023. "Can one hear the shape of a target zone?," Journal of Mathematical Economics, Elsevier, vol. 107(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. Chateauneuf, A. & Lakhnati, G., 2015. "Increases in risk and demand for a risky asset," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 44-48.
    2. 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.
    3. Jean Baccelli & Georg Schollmeyer & Christoph Jansen, 2022. "Risk aversion over finite domains," Theory and Decision, Springer, vol. 93(2), pages 371-397, September.
    4. Claudio Bonilla & Marcos Vergara, 2022. "New results on precautionary saving and nonlinear risks," Journal of Economics, Springer, vol. 136(2), pages 177-189, July.
    5. Grant, Simon & Quiggin, John, 2005. "Increasing uncertainty: a definition," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 117-141, March.
    6. Chiu, W. Henry, 2019. "Comparative statics in an ordinal theory of choice under risk," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 113-123.
    7. 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.
    8. Turan G. Bali & Nusret Cakici & Fousseni Chabi-Yo, 2011. "A Generalized Measure of Riskiness," Management Science, INFORMS, vol. 57(8), pages 1406-1423, August.
    9. Gajdos, Thibault & Weymark, John A., 2012. "Introduction to inequality and risk," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1313-1330.
    10. Muller, Alfred, 1998. "Comparing risks with unbounded distributions," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 229-239, September.
    11. Sudhir A. Shah, 2010. "Comparative Riskiness Of Random Vector Outcomes," Working papers 191, Centre for Development Economics, Delhi School of Economics.
    12. Kwanho Shin & Jaewoo Lee, 2000. "The Role of a Variable Input in the Relationship between Investment and Uncertainty," American Economic Review, American Economic Association, vol. 90(3), pages 667-680, June.
    13. Pereira, Rodrigo Mendes, 2008. "Investment and Uncertainty in Machinery and Real Estate," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 62(3), November.
    14. Thomas Paulsson & Robert Sproule & Andreas Wagener, 2005. "The Demand For A Risky Asset: Signing, Jointly And Separately, The Effects Of Three Distributional Shifts," Metroeconomica, Wiley Blackwell, vol. 56(2), pages 221-232, May.
    15. Marco de Pinto & Laszlo Goerke, 2022. "Cost uncertainty in an oligopoly with endogenous entry," Bulletin of Economic Research, Wiley Blackwell, vol. 74(4), pages 927-948, October.
    16. Pedro Rui Mazeda Gil, 2005. "The Firm’s Perception of Demand Shocks and the Expected Profitability of Capital under Uncertainty," FEP Working Papers 195, Universidade do Porto, Faculdade de Economia do Porto.
    17. Andrew B. Abel & Janice C. Eberly, "undated". "An Exact Solution for the Investment and Market Value of a Firm Facing Uncertainty, Adjustment Costs, and Irreversibility," Rodney L. White Center for Financial Research Working Papers 12-93, Wharton School Rodney L. White Center for Financial Research.
    18. Mark Huggett, 2004. "Precautionary Wealth Accumulation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 769-781.
    19. Snow, Arthur, 2003. "Substitution and income effects for increases in risk," Economics Letters, Elsevier, vol. 79(3), pages 313-317, June.
    20. Hjalmar Böhm & Michael Funke, 2001. "Does the Nominal Exchange Rate Regime Matter for Investment?," Quantitative Macroeconomics Working Papers 20105, Hamburg University, Department of Economics.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:mateco:v:86:y:2020:i:c:p:69-82. 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.