Weighted Scoring Rules and Convex Risk Measures

• 成果类型: Article
• 署名作者: Smith, Zachary J.; Bickel, J. Eric
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.2190
• 发表日期: 2022
• 页码: 3371-3385
• 关键词: utility; entropy

摘要

This paper establishes a new relationship between proper scoring rules and convex risk measures. Specifically, we demonstrate that the entropy function associated with any weighted scoring rule is equal to the maximum value of an optimization problem where an investor maximizes a concave certainty equivalent (the negation of a convex risk measure). Using this connection, we construct two classes of proper weighted scoring rules with associated entropy functions based on phi-divergences. These rules are generalizations of the weighted power and weighted pseudospherical rules.