IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v69y2024ipas1544612324010729.html
   My bibliography  Save this article

Approximate utility

Author

Listed:
  • Dybvig, Philip H.
  • Li, Shu

Abstract

Approximating arbitrage or a perfect hedge in a limit implies approximation in utility (formally, expected utilities are continuous in L2), if and only if the utility function is bounded above and below by quadratics. We characterize when some special utility functions are continuous for all random consumptions with a common lower bound. Only linear, quadratic, and, in some cases, translated SAHARA utilities are continuous if there is no lower bound. We also characterize when a utility function defined on a convex subset can be extended to an L2-continuous nondecreasing and concave utility function on all of R.

Suggested Citation

  • Dybvig, Philip H. & Li, Shu, 2024. "Approximate utility," Finance Research Letters, Elsevier, vol. 69(PA).
    • Handle: RePEc:eee:finlet:v:69:y:2024:i:pa:s1544612324010729
    DOI: 10.1016/j.frl.2024.106042
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612324010729
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2024.106042?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. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    2. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    3. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    4. Dybvig, Philip & Liu, Fang, 2018. "On investor preferences and mutual fund separation," Journal of Economic Theory, Elsevier, vol. 174(C), pages 224-260.
    5. Samuelson, Paul A., 1967. "General Proof that Diversification Pays*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(1), pages 1-13, March.
    6. Chen, An & Pelsser, Antoon & Vellekoop, Michel, 2011. "Modeling non-monotone risk aversion using SAHARA utility functions," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2075-2092, 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. 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.
    2. Tourky, Rabee, 1999. "Production equilibria in locally proper economies with unbounded and unordered consumers," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 303-315, November.
    3. Michele Costola & Bertrand Maillet & Zhining Yuan & Xiang Zhang, 2024. "Mean–variance efficient large portfolios: a simple machine learning heuristic technique based on the two-fund separation theorem," Annals of Operations Research, Springer, vol. 334(1), pages 133-155, March.
    4. Gianluca Cassese, 2021. "Complete and competitive financial markets in a complex world," Finance and Stochastics, Springer, vol. 25(4), pages 659-688, October.
    5. Ni, Jian & Chu, Lap-Keung & Yen, Benjamin P.C., 2016. "Coordinating operational policy with financial hedging for risk-averse firms," Omega, Elsevier, vol. 59(PB), pages 279-289.
    6. Elyès Jouini & Clotilde Napp, 2002. "Arbitrage Pricing And Equilibrium Pricing: Compatibility Conditions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume III), chapter 6, pages 131-158, World Scientific Publishing Co. Pte. Ltd..
    7. Moris S. Strub & Xun Yu Zhou, 2021. "Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes," Finance and Stochastics, Springer, vol. 25(2), pages 331-358, April.
    8. Yicheng Wei & Junzo Watada & Zijin Wang, 2025. "Topology Unveiled: A New Horizon for Economic and Financial Modeling," Mathematics, MDPI, vol. 13(2), pages 1-34, January.
    9. Dybvig, Philip & Liu, Fang, 2018. "On investor preferences and mutual fund separation," Journal of Economic Theory, Elsevier, vol. 174(C), pages 224-260.
    10. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    11. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, February.
    12. Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998. "Portfolio dominance and optimality in infinite security markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 347-366, October.
    13. repec:dau:papers:123456789/5590 is not listed on IDEAS
    14. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    15. Annabi, Amira & Breton, Michèle & François, Pascal, 2012. "Resolution of financial distress under Chapter 11," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1867-1887.
    16. Angrisani, Marco & Atella, Vincenzo & Brunetti, Marianna, 2018. "Public health insurance and household portfolio Choices: Unravelling financial “Side Effects” of Medicare," Journal of Banking & Finance, Elsevier, vol. 93(C), pages 198-212.
    17. Askoura, Youcef & Billot, Antoine, 2021. "Social decision for a measure society," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    18. Jun Liu, 2004. "Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities," The Review of Financial Studies, Society for Financial Studies, vol. 17(3), pages 611-641.
    19. Gollier, Christian, 2002. "Time Horizon and the Discount Rate," Journal of Economic Theory, Elsevier, vol. 107(2), pages 463-473, December.
    20. Chen, An & Hieber, Peter & Sureth, Caren, 2022. "Pay for tax certainty? Advance tax rulings for risky investment under multi-dimensional tax uncertainty," arqus Discussion Papers in Quantitative Tax Research 273, arqus - Arbeitskreis Quantitative Steuerlehre.
    21. Raffestin, Louis, 2014. "Diversification and systemic risk," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 85-106.

    More about this item

    Keywords

    Approximate utility; Properness; von Neumann-Morgenstern; Quadratic utility;
    All these keywords.

    JEL classification:

    • G0 - Financial Economics - - General
    • C0 - Mathematical and Quantitative Methods - - General
    • D0 - Microeconomics - - General

    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:finlet:v:69:y:2024:i:pa:s1544612324010729. 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/frl .

    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.