The Foster-Hart measure of riskiness for general gambles

• 成果类型: Article
• 署名作者: Riedel, Frank; Hellmann, Tobias
• 署名单位: University of Bielefeld
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE1499
• 发表日期: 2015-01-01
• 页码: 1-9
• 关键词: Risk measures; bankruptcy; continuous random variable

摘要

Foster and Hart propose a measure of riskiness for discrete random variables. Their defining equation has no solution for many common continuous distributions. We show how to extend consistently the definition of riskiness to continuous random variables. For many continuous random variables, the risk measure is equal to the worst-case risk measure, i.e., the maximal possible loss incurred by that gamble. For many discrete gambles with a large number of values, the Foster-Hart riskiness is close to the maximal loss. We give a simple characterization of gambles whose riskiness is or is close to the maximal loss.