A Theorem Proofs

The decision maker is risk-neutral, therefore we can choose u(v) = v; note that utility functions can be modified by linear transformations without changing the certain equivalent. This means that certain equivalents and expected values are equivalent. We drop the policy superscript in all relevant expressions for notational simplicity. We use a property of the exponential utility function around linear tranformation: if every reward is augmented by a constant amount, then the certain equivalent increases by that constant amount. In general, this holds only for linear and exponential utility functions as they are the only ones satisfying constant risk aversion.