The Erroneous Approximation of Expected Utility by Means of a Taylor's Series Expansion: Analytic and Computational Results

Abstract

where y is the investor's wealth, which is a random variable, y is the expected wealth, U(y) is the utility function, f(y) the probability density function, and pi the discrete probability. The calculation can be performed without any difficulties in the discrete case. The expected value of utility is a simple addition of the weighted utility-arguments U(yi)pi. In the continuous case, for some special cases, computing can be done by direct analytic integration. A standard device for computing the value of integral (1) is a Taylor's series expansion around the expected value y (see Paul Samuelson and S. C. Tsiang). Expressing the value of utility U(y) for the argument y, we obtain

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