Weighted Scoring Rules and Convex Risk Measures
建立了加权评分规则与凸风险度量之间的通用联系，通过示例展示了基于phi-散度的加权评分规则族及其对应的风险度量，对评估主观概率预测和金融风险管理有参考价值。
In Weighted Scoring Rules and Convex Risk Measures, Dr. Zachary J. Smith and Prof. J. Eric Bickel (both at the University of Texas at Austin) present a general connection between weighted proper scoring rules and investment decisions involving the minimization of a convex risk measure. Weighted scoring rules are quantitative tools for evaluating the accuracy of probabilistic forecasts relative to a baseline distribution. In their paper, the authors demonstrate that the relationship between convex risk measures and weighted scoring rules relates closely with previous economic characterizations of weighted scores based on expected utility maximization. As illustrative examples, the authors study two families of weighted scoring rules based on phi-divergences (generalizations of the Weighted Power and Weighted Pseudospherical Scoring rules) along with their corresponding risk measures. The paper will be of particular interest to the decision analysis and mathematical finance communities as well as those interested in the elicitation and evaluation of subjective probabilistic forecasts.