IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v208y2013i1p417-43210.1007-s10479-012-1066-9.html
   My bibliography  Save this article

Discounting axioms imply risk neutrality

Author

Listed:
  • Matthew Sobel

Abstract

Although most applications of discounting occur in risky settings, the best-known axiomatic justifications are deterministic. This paper provides an axiomatic rationale for discounting in a stochastic framework. Consider a representation of time and risk preferences with a binary relation on a real vector space of vector-valued discrete-time stochastic processes on a probability space. Four axioms imply that there are unique discount factors such that preferences among stochastic processes correspond to preferences among present value random vectors. The familiar axioms are weak ordering, continuity and nontriviality. The fourth axiom, decomposition, is non-standard and key. These axioms and the converse of decomposition are assumed in previous axiomatic justifications for discounting with nonlinear intraperiod utility functions in deterministic frameworks. Thus, the results here provide the weakest known sufficient conditions for discounting in deterministic or stochastic settings. In addition to the four axioms, if there exists a von Neumann-Morgenstern utility function corresponding to the binary relation, then that function is risk neutral (i.e., affine). In this sense, discounting axioms imply risk neutrality. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Matthew Sobel, 2013. "Discounting axioms imply risk neutrality," Annals of Operations Research, Springer, vol. 208(1), pages 417-432, September.
  • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:417-432:10.1007/s10479-012-1066-9
    DOI: 10.1007/s10479-012-1066-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1066-9
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10479-012-1066-9?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. Eugene A. Feinberg & Adam Shwartz, 1994. "Markov Decision Models with Weighted Discounted Criteria," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 152-168, February.
    2. Ludger Linnemann & Andreas Schabert, 2010. "Debt Nonneutrality, Policy Interactions, And Macroeconomic Stability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(2), pages 461-474, May.
    3. Michael Magill & Martine Quinzii, 2010. "A Comoment Criterion For The Choice Of Risky Investment By Firms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(3), pages 723-744, August.
    4. Cyrus Derman, 1962. "On Sequential Decisions and Markov Chains," Management Science, INFORMS, vol. 9(1), pages 16-24, October.
    5. Balcer, Yves & Lippman, Steven A., 1984. "Technological expectations and adoption of improved technology," Journal of Economic Theory, Elsevier, vol. 34(2), pages 292-318, December.
    6. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    7. Pedro S. Amaral & Erwan Quintin, 2010. "Limited Enforcement, Financial Intermediation, And Economic Development: A Quantitative Assessment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(3), pages 785-811, August.
    8. Nagata Furukawa, 1980. "Characterization of Optimal Policies in Vector-Valued Markovian Decision Processes," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 271-279, May.
    9. John M. Miyamoto & Peter Wakker, 1996. "Multiattribute Utility Theory Without Expected Utility Foundations," Operations Research, INFORMS, vol. 44(2), pages 313-326, April.
    10. Charles E. Blair, 1984. "Axioms and Examples Related to Ordinal Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 9(3), pages 345-347, August.
    11. Ellen R. M cG rattan & Lee E. Ohanian, 2010. "Does Neoclassical Theory Account For The Effects Of Big Fiscal Shocks? Evidence From World War Ii," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(2), pages 509-532, May.
    12. A. C. Williams & J. I. Nassar, 1966. "Financial Measurement of Capital Investments," Management Science, INFORMS, vol. 12(11), pages 851-864, July.
    13. Frederic H. Murphy & Michael A. Toman & Howard J. Weiss, 1989. "A Dynamic Nash Game Model of Oil Market Disruption and Strategic Stockpiling," Operations Research, INFORMS, vol. 37(6), pages 958-971, December.
    14. Larry E. Jones & Alice Schoonbroodt, 2010. "Complements Versus Substitutes And Trends In Fertility Choice In Dynastic Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(3), pages 671-699, August.
    15. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    16. Johnsen, Thore H & Donaldson, John B, 1985. "The Structure of Intertemporal Preferences under Uncertainty and Time Consistent Plans," Econometrica, Econometric Society, vol. 53(6), pages 1451-1458, November.
    17. James S. Dyer & Rakesh K. Sarin, 1979. "Measurable Multiattribute Value Functions," Operations Research, INFORMS, vol. 27(4), pages 810-822, August.
    18. M. Shubik & M. J. Sobel, 1992. "On Matching Book: A Problem in Banking and Corporate Finance," Management Science, INFORMS, vol. 38(6), pages 827-839, June.
    19. David M. Kreps & Evan L. Porteus, 2013. "Temporal von Neumann—Morgenstern and Induced Preferences," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 11, pages 181-206, World Scientific Publishing Co. Pte. Ltd..
    20. Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
    21. Matthew J. Sobel, 1975. "Ordinal Dynamic Programming," Management Science, INFORMS, vol. 21(9), pages 967-975, May.
    22. Martin Shubik, 1970. "Game theory, behavior, and the paradox of the Prisoner's Dilemma: three solutions," Journal of Conflict Resolution, Peace Science Society (International), vol. 14(2), pages 181-193, June.
    23. Epstein, Larry G., 1983. "Stationary cardinal utility and optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 31(1), pages 133-152, October.
    24. George E. Monahan, 1983. "Optimal Advertising with Stochastic Demand," Management Science, INFORMS, vol. 29(1), pages 106-117, January.
    25. Jörgen W. Weibull, 1985. "Discounted-Value Representations of Temporal Preferences," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 244-250, May.
    26. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    27. Feinberg, Eugene A. & Park, Haechurl, 1994. "Finite state Markov decision models with average reward criteria," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 159-177, January.
    28. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
    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. Lucy Gongtao Chen & Daniel Zhuoyu Long & Melvyn Sim, 2015. "On Dynamic Decision Making to Meet Consumption Targets," Operations Research, INFORMS, vol. 63(5), pages 1117-1130, October.
    2. Amanda M. White & Pelin G. Canbolat, 2018. "Finite‐horizon Markov population decision chains with constant risk posture," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 580-593, December.
    3. Kitti, Mitri, 2018. "Sustainable social choice under risk," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 19-31.
    4. Marc St-Pierre, 2017. "Risk-induced discounting," Theory and Decision, Springer, vol. 82(1), pages 13-30, January.

    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. Lex Borghans & Angela Lee Duckworth & James J. Heckman & Bas ter Weel, 2008. "The Economics and Psychology of Personality Traits," Journal of Human Resources, University of Wisconsin Press, vol. 43(4).
    2. Dorian Jullien, 2018. "Under Risk, Over Time, Regarding Other People: Language and Rationality within Three Dimensions," Research in the History of Economic Thought and Methodology, in: Including a Symposium on Latin American Monetary Thought: Two Centuries in Search of Originality, volume 36, pages 119-155, Emerald Group Publishing Limited.
    3. Hammond, Peter J & Zank, Horst, 2013. "Rationality and Dynamic Consistency under Risk and Uncertainty," The Warwick Economics Research Paper Series (TWERPS) 1033, University of Warwick, Department of Economics.
    4. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    5. Günter Bamberg & Michael Krapp, 2016. "Is time consistency compatible with risk aversion?," Review of Managerial Science, Springer, vol. 10(2), pages 195-211, March.
    6. Obara, Ichiro & Park, Jaeok, 2017. "Repeated games with general discounting," Journal of Economic Theory, Elsevier, vol. 172(C), pages 348-375.
    7. Ned Augenblick & Muriel Niederle & Charles Sprenger, 2013. "Working Over Time: Dynamic Inconsistency in Real Effort Tasks," NBER Working Papers 18734, National Bureau of Economic Research, Inc.
    8. Antony Millner & Geoffrey Heal, 2015. "Collective intertemporal choice: time consistency vs. time invariance," GRI Working Papers 220, Grantham Research Institute on Climate Change and the Environment.
    9. Luc Arrondel & André Masson & Daniel Verger, 2004. "De la théorie à une enquête méthodologique originale," Économie et Statistique, Programme National Persée, vol. 374(1), pages 21-51.
    10. Dorian Jullien, 2016. "Under Uncertainty, Over Time and Regarding Other People: Rationality in 3D," GREDEG Working Papers 2016-20, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    11. Ying He & James S. Dyer & John C. Butler, 2013. "On the Axiomatization of the Satiation and Habit Formation Utility Models," Operations Research, INFORMS, vol. 61(6), pages 1399-1410, December.
    12. Drouhin, Nicolas, 2015. "A rank-dependent utility model of uncertain lifetime," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 208-224.
    13. Min Gong & David Krantz & Elke Weber, 2014. "Why Chinese discount future financial and environmental gains but not losses more than Americans," Journal of Risk and Uncertainty, Springer, vol. 49(2), pages 103-124, October.
    14. Ida, Takanori & Goto, Rei & Takahashi, Yuko & Nishimura, Shuzo, 2011. "Can economic-psychological parameters predict successful smoking cessation?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 40(3), pages 285-295, May.
    15. Schilirò, Daniele & Graziano, Mario, 2011. "Scelte e razionalità nei modelli economici: un'analisi multidisciplinare [Choices and rationality in economic models: a multidisciplinary analysis]," MPRA Paper 31910, University Library of Munich, Germany.
    16. Jindrich Matousek & Tomas Havranek & Zuzana Irsova, 2022. "Individual discount rates: a meta-analysis of experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 25(1), pages 318-358, February.
    17. Hansen, Anders Chr., 2006. "Do declining discount rates lead to time inconsistent economic advice?," Ecological Economics, Elsevier, vol. 60(1), pages 138-144, November.
    18. Meyer, Andrew G., 2015. "The impacts of elicitation mechanism and reward size on estimated rates of time preference," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 58(C), pages 132-148.
    19. Giles W Story & Ivaylo Vlaev & Ben Seymour & Joel S Winston & Ara Darzi & Raymond J Dolan, 2013. "Dread and the Disvalue of Future Pain," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-18, November.
    20. Pier-André Bouchard St-Amant & Jean-Denis Garon, 2015. "Optimal redistributive pensions and the cost of self-control," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 22(5), pages 723-740, October.

    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:spr:annopr:v:208:y:2013:i:1:p:417-432:10.1007/s10479-012-1066-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.