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Discounting Models for Outcomes over Continuous Time

Author

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  • Charles M. Harvey

    (University of Houston)

  • Lars Peter Østerdal

    (Department of Economics, University of Copenhagen)

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

  • Charles M. Harvey & Lars Peter Østerdal, 2011. "Discounting Models for Outcomes over Continuous Time," Discussion Papers 11-12, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:1112
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    References listed on IDEAS

    as
    1. Charles M. Harvey, 1986. "Value Functions for Infinite-Period Planning," Management Science, INFORMS, vol. 32(9), pages 1123-1139, September.
    2. Charles Harvey, 1995. "Proportional Discounting of Future Costs and Benefits," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 381-399, May.
    3. 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.
    4. 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.
    5. A. C. Williams & J. I. Nassar, 1966. "Financial Measurement of Capital Investments," Management Science, INFORMS, vol. 12(11), pages 851-864, July.
    6. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    7. Harvey, Charles M., 1994. "The reasonableness of non-constant discounting," Journal of Public Economics, Elsevier, vol. 53(1), pages 31-51, January.
    8. Jörgen W. Weibull, 1985. "Discounted-Value Representations of Temporal Preferences," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 244-250, May.
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    Citations

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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. Webb, Craig S., 2016. "Continuous quasi-hyperbolic discounting," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 99-106.
    4. Hara, Kazuhiro, 2016. "Characterization of stationary preferences in a continuous time framework," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 34-43.
    5. Pavlo Blavatskyy, 2020. "Expected discounted utility," Theory and Decision, Springer, vol. 88(2), pages 297-313, March.

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    More about this item

    Keywords

    continuous time; integral discounting; integral value or utility function;
    All these keywords.

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