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Discounting models for outcomes over continuous time

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  • Harvey, Charles M.
  • Østerdal, Lars Peter

Abstract

Events that occur over a period of time can be described either as sequences of outcomes at discrete times or as functions of outcomes in an interval of time. This paper presents discounting models for events of the latter type. Conditions on preferences are shown to be satisfied if and only if the preferences are represented by a function that is an integral of a discounting function times a scale defined on outcomes at instants of time.

Suggested Citation

  • Harvey, Charles M. & Østerdal, Lars Peter, 2012. "Discounting models for outcomes over continuous time," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 284-294.
    • Handle: RePEc:eee:mateco:v:48:y:2012:i:5:p:284-294
    DOI: 10.1016/j.jmateco.2012.07.001
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    References listed on IDEAS

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    1. Charles Harvey, 1995. "Proportional Discounting of Future Costs and Benefits," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 381-399, May.
    2. Charles M. Harvey & Lars Peter Østerdal, 2007. "Integral-Value Models for Outcomes over Continuous Time," Discussion Papers 07-10, University of Copenhagen. Department of Economics.
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    5. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    6. W. M. Gorman, 1968. "The Structure of Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 367-390.
    7. A. C. Williams & J. I. Nassar, 1966. "Financial Measurement of Capital Investments," Management Science, INFORMS, vol. 12(11), pages 851-864, July.
    8. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
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    Cited by:

    1. Drouhin, Nicolas, 2020. "Non-stationary additive utility and time consistency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 1-14.
    2. Marcus Pivato, 2021. "Intertemporal Choice with Continuity Constraints," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 1203-1229, August.
    3. Lorenzo Bastianello & Vassili Vergopoulos, 2024. "Discounted Subjective Expected Utility in Continuous Time," Papers 2403.15319, arXiv.org.
    4. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    5. Hara, Kazuhiro, 2016. "Characterization of stationary preferences in a continuous time framework," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 34-43.
    6. Pavlo Blavatskyy, 2020. "Expected discounted utility," Theory and Decision, Springer, vol. 88(2), pages 297-313, March.

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