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摘要翻译：
Foster和Hart提出了离散随机变量风险的操作度量。我们证明了它们的定义方程对于包括许多均匀分布在内的许多常见的连续分布是无解的，例如，我们证明了如何一致地将风险的定义推广到连续随机变量。对于许多连续随机变量，风险测度等于最坏情况下的风险测度，即该赌博所引起的最大可能损失。我们还将Foster-Hart风险测度推广到一般分布和概率空间的动态环境中，并证明了推广的测度在无限重复的赌博中避免了破产。
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英文标题：
《The Foster-Hart Measure of Riskiness for General Gambles》
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作者：
Frank Riedel and Tobias Hellmann
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最新提交年份：
2013
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions including many uniform distributions, e.g. 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. We also extend the Foster--Hart risk measure to dynamic environments for general distributions and probability spaces, and we show that the extended measure avoids bankruptcy in infinitely repeated gambles.
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PDF链接：
https://arxiv.org/pdf/1301.1471
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