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A property of preferences that causes an agent to prefer alternatives whose outcomes are relatively certain, even when the associated expected payoff is lower.

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Proof: Risk averse; Certainty Equivalent smaller than expected value

I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds: The certainty equivalent, $CE(\cdot)$, is sm …