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Mean variance preferences and the heat equation

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Abstract

Chipman (1979) proves that for an expected utility maximizer choosing from a domain of normal distributions with mean μ and variance σ2 the induced preference functionV(μ, σ) satisfies a differential equation known as the heat equation. The purpose of this note is to provide a generalization and simple proof of this result which does not depend on the normality assumption.

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Bardsley, P. Mean variance preferences and the heat equation. Theor Decis 35, 199–202 (1993). https://doi.org/10.1007/BF01074959

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  • DOI: https://doi.org/10.1007/BF01074959

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