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Expected Utility and the Truncated Normal Distribution

Listed author(s):
  • R. Norgaard

    (University of Connecticut)

  • T. Killeen

    (University of Connecticut)

Registered author(s):

    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.

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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 26 (1980)
    Issue (Month): 9 (September)
    Pages: 901-909

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    Handle: RePEc:inm:ormnsc:v:26:y:1980:i:9:p:901-909
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