An Analytical Comparison of Certainty Equivalence and Sequential Updating

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Abstract
This article analyzes the differences between the certainty equivalence (CE) and the sequential updating (SU) approach to the problem of multiperiod decision-making under uncertainty. It is assumed that a single target variable, y, depends linearly on a single control variable, x, and an additive and normally distributed disturbance term, u. It is proved that the expected loss associated with CE is infinite, while that associated with SU is bounded above. Moreover, it is shown that truncation of the distribution of the target variable y may result in the convergence of the expected loss associated with CE.

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