ASYMMETRIC LOSS FUNCTION AND OPTIMAL POLICY UNDER UNCERTAINTY: A SIMPLE PROOF
针对非对称准凸损失函数和对称准凹概率密度函数，给出了一个极简证明，表明政策制定者应选择损失函数中损害较小一侧的政策值以最小化期望损失。该证明适用于多种损失函数和概率密度函数，并扩展到对称损失与非对称概率密度函数等情形。
Abstract Given an asymmetric quasi‐convex loss function and a symmetric quasi‐concave probability density function, both continuous, an extremely simple proof is suggested that shows that a policy maker will minimize expected loss by choosing a policy value on the less‐damaging side of the loss function. This proof, which is compatible with a wide variety of loss functions and probability density functions, is extended to include cases where a symmetric loss function is matched against an asymmetric probability density function and where an asymmetric loss is matched with an asymmetric probability density function.