Implicit Mean Value and Certainty Equivalence
研究一种由概率测度隐式定义的广义均值,给出其刻画条件并讨论与确定性等价的关系,适合对决策理论或风险度量感兴趣的学者。
This paper considers a generalized mean value m(p) defined implicitly for a probability measure p on the reals as the unique y for which J +(x, y) dp(x) = 0, where 0 is skewsymmetric and strictly increasing in its first argument. Conditions on m that are necessary and sufficient for the implicit characterization are given and its relationship to certainty equivalence is discussed.