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Expected Utility and the Truncated Normal Distribution


  • R. Norgaard

    (University of Connecticut)

  • T. Killeen

    (University of Connecticut)


This article demonstrates that: (1) When a normally distributed decision variable is combined with an analytic utility function (one with derivatives of all orders and a power series expansion involving those derivatives), the expected utility can be expressed in powers of \mu and \sigma 2 . (2) In the case of the normal model, when the tails of the distribution do not reflect reality in the mind of a decision-maker, a truncated normal model is a possible alternative. (3) If the appropriate model is the truncated normal distribution, then the expected utility is approximately a linear function of \mu and \sigma for several important classes of risk averse utility functions. (4) The negative exponential is an especially useful utility function since it has a simple closed form for both the truncated and nontruncated models, and since it gives an ordering similar to those of the log, arctangent or power utility functions.

Suggested Citation

  • R. Norgaard & T. Killeen, 1980. "Expected Utility and the Truncated Normal Distribution," Management Science, INFORMS, vol. 26(9), pages 901-909, September.
  • Handle: RePEc:inm:ormnsc:v:26:y:1980:i:9:p:901-909

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    Cited by:

    1. Maria Osipenko & Zhiwei Shen & Martin Odening, 2015. "Is there a demand for multi-year crop insurance?," Agricultural Finance Review, Emerald Group Publishing, vol. 75(1), pages 92-102, May.
    2. Alexander, Peter & Moran, Dominic, 2013. "Impact of perennial energy crops income variability on the crop selection of risk averse farmers," Energy Policy, Elsevier, vol. 52(C), pages 587-596.


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