IDEAS home Printed from https://ideas.repec.org/p/zbw/safewp/17.html
   My bibliography  Save this paper

Stochastic differential utility as the continuous-time limit of recursive utility

Author

Listed:
  • Kraft, Holger
  • Seifried, Frank Thomas

Abstract

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Duffie and Epstein (1992), in the continuous-time limit of vanishing grid size.

Suggested Citation

  • Kraft, Holger & Seifried, Frank Thomas, 2013. "Stochastic differential utility as the continuous-time limit of recursive utility," SAFE Working Paper Series 17, Leibniz Institute for Financial Research SAFE.
    • Handle: RePEc:zbw:safewp:17
    DOI: 10.2139/ssrn.2264293
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/88743/1/775703109.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.2139/ssrn.2264293?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
    ---><---

    References listed on IDEAS

    as
    1. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    2. Weil, Philippe, 1989. "The equity premium puzzle and the risk-free rate puzzle," Journal of Monetary Economics, Elsevier, vol. 24(3), pages 401-421, November.
    3. Obstfeld, Maurice, 1994. "Evaluating risky consumption paths: The role of intertemporal substitutability," European Economic Review, Elsevier, vol. 38(7), pages 1471-1486, August.
    4. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
    5. Lars Peter Hansen & John C. Heaton & Nan Li, 2008. "Consumption Strikes Back? Measuring Long-Run Risk," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 260-302, April.
    6. Larry G. Epstein & Stanley E. Zin, 2013. "Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 12, pages 207-239, World Scientific Publishing Co. Pte. Ltd..
    7. Svensson, Lars E. O., 1989. "Portfolio choice with non-expected utility in continuous time," Economics Letters, Elsevier, vol. 30(4), pages 313-317, October.
    8. Fatih Guvenen, 2009. "A Parsimonious Macroeconomic Model for Asset Pricing," Econometrica, Econometric Society, vol. 77(6), pages 1711-1750, November.
    9. Xavier Gabaix, 2012. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(2), pages 645-700.
    10. Bouchard, Bruno & Elie, Romuald, 2008. "Discrete-time approximation of decoupled Forward-Backward SDE with jumps," Stochastic Processes and their Applications, Elsevier, vol. 118(1), pages 53-75, January.
    11. TallariniJr., Thomas D., 2000. "Risk-sensitive real business cycles," Journal of Monetary Economics, Elsevier, vol. 45(3), pages 507-532, June.
    12. Georg Kaltenbrunner & Lars A. Lochstoer, 2010. "Long-Run Risk through Consumption Smoothing," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3190-3224, August.
    13. Mark Fisher & Christian Gilles, 1998. "Consumption and asset prices and recursive preferences," Finance and Economics Discussion Series 1998-40, Board of Governors of the Federal Reserve System (U.S.).
    14. repec:bla:jfinan:v:59:y:2004:i:4:p:1481-1509 is not listed on IDEAS
    15. Schroder, Mark & Skiadas, Costis, 1999. "Optimal Consumption and Portfolio Selection with Stochastic Differential Utility," Journal of Economic Theory, Elsevier, vol. 89(1), pages 68-126, November.
    16. Marinacci, Massimo & Montrucchio, Luigi, 2010. "Unique solutions for stochastic recursive utilities," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1776-1804, September.
    17. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    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. Kraft, Holger & Seifried, Frank Thomas, 2014. "Stochastic differential utility as the continuous-time limit of recursive utility," Journal of Economic Theory, Elsevier, vol. 151(C), pages 528-550.
    2. Yu Chen & Thomas Cosimano & Alex Himonas & Peter Kelly, 2014. "An Analytic Approach for Stochastic Differential Utility for Endowment and Production Economies," Computational Economics, Springer;Society for Computational Economics, vol. 44(4), pages 397-443, December.
    3. Patrick Augustin & Roméo Tédongap, 2021. "Disappointment Aversion, Term Structure, and Predictability Puzzles in Bond Markets," Management Science, INFORMS, vol. 67(10), pages 6266-6293, October.
    4. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Permanent Income and Pricing," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 3, pages 33-81, World Scientific Publishing Co. Pte. Ltd..
    5. Knut K. Aase & Petter Bjerksund, 2021. "The Optimal Spending Rate versus the Expected Real Return of a Sovereign Wealth Fund," JRFM, MDPI, vol. 14(9), pages 1-36, September.
    6. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    7. Ravi Bansal & Ivan Shaliastovich, 2010. "Confidence Risk and Asset Prices," American Economic Review, American Economic Association, vol. 100(2), pages 537-541, May.
    8. David K. Backus & Bryan R. Routledge & Stanley E. Zin, 2005. "Exotic Preferences for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2004, Volume 19, pages 319-414, National Bureau of Economic Research, Inc.
    9. George M. Constantinides, 2017. "Asset Pricing: Models and Empirical Evidence," Journal of Political Economy, University of Chicago Press, vol. 125(6), pages 1782-1790.
    10. Li, Minqiang, 2010. "Asset Pricing - A Brief Review," MPRA Paper 22379, University Library of Munich, Germany.
    11. Kliem, Martin & Uhlig, Harald, 2013. "Bayesian estimation of a DSGE model with asset prices," Discussion Papers 37/2013, Deutsche Bundesbank.
    12. John List & Harald Uhlig, 2017. "Introduction," Journal of Political Economy, University of Chicago Press, vol. 125(6), pages 1723-1727.
    13. Ufuk Akcigit & Fernando Alvarez & Stephane Bonhomme & George M Constantinides & Douglas W Diamond & Eugene F Fama & David W Galenson & Michael Greenstone & Lars Peter Hansen & Uhlig Harald & James J H, 2017. "The Past, Present, and Future of Economics: A Celebration of the 125-Year Anniversary of the JPE and of Chicago Economics," Natural Field Experiments 00635, The Field Experiments Website.
    14. Alfonso Irarrazabal & Juan Carlos Parra-Alvarez, 2015. "Time-varying disaster risk models: An empirical assessment of the Rietz-Barro hypothesis," CREATES Research Papers 2015-08, Department of Economics and Business Economics, Aarhus University.
    15. Smith, William & Son, Young Seob, 2005. "Can the desire to conserve our natural resources be self-defeating?," Journal of Environmental Economics and Management, Elsevier, vol. 49(1), pages 52-67, January.
    16. Luca De Gennaro Aquino & Sascha Desmettre & Yevhen Havrylenko & Mogens Steffensen, 2024. "Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time," Papers 2407.16525, arXiv.org, revised Oct 2024.
    17. Beeler, Jason & Campbell, John Y., 2012. "The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment," Critical Finance Review, now publishers, vol. 1(1), pages 141-182, January.
    18. Lars Lochstoer & Harjoat S. Bhamra, 2009. "Return Predictability and Labor Market Frictions in a Real Business Cycle Model," 2009 Meeting Papers 1257, Society for Economic Dynamics.
    19. Isaenko, Sergei, 2008. "The term structure of interest rates in a pure exchange economy where investors have heterogeneous recursive preferences," The Quarterly Review of Economics and Finance, Elsevier, vol. 48(3), pages 457-481, August.
    20. Isoré, Marlène & Szczerbowicz, Urszula, 2017. "Disaster risk and preference shifts in a New Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 97-125.

    More about this item

    Keywords

    Stochastic differential utility; recursive utility; convergence; backward stochastic differential equation;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:zbw:safewp:17. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/csafede.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.