Scoring Rules, Generalized Entropy, and Utility Maximization
成果类型：
Article
署名作者：
Jose, Victor Richmond R.; Nau, Robert F.; Winkler, Robert L.
署名单位：
Duke University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1070.0498
发表日期：
2008
页码：
1146-1157
关键词：
摘要：
Information measures arise in many disciplines, including forecasting (where scoring rules are used to provide incentives for probability estimation), signal processing (where information gain is measured in physical units of relative entropy), decision analysis (where new information can lead to improved decisions), and finance (where investors optimize portfolios based on their private information and risk preferences). In this paper, we generalize the two most commonly used parametric families of scoring rules and demonstrate their relation to well-known generalized entropies and utility functions, shedding new light on the characteristics of alternative scoring rules as well as duality relationships between utility maximization and entropy minimization. In particular, we show that weighted forms of the pseudospherical and power scoring rules correspond exactly to measures of relative entropy (divergence) with convenient properties, and they also correspond exactly to the solutions of expected utility maximization problems in which a risk-averse decision maker whose utility function belongs to the linear-risk-tolerance family interacts with a risk-neutral betting opponent or a complete market for contingent claims in either a one-period or a two-period setting. When the market is incomplete, the corresponding problems of maximizing linear-risk-tolerance utility with the risk-tolerance coeffient beta are the duals of the problems of minimizing the pseudospherical or power divergence of order beta between the decision maker's subjective probability distribution and the set of risk-neutral distributions that support asset prices.