一般赌博的Foster-Hart风险度量
The Foster-Hart Measure of Riskiness for General Gambles
摘要：
Foster和Hart提出了离散随机变量风险的操作度量。我们表明，他们的定义方程没有解决方案，许多常见的连续分布，包括许多均匀分布，例如，我们展示了如何一致地扩展定义的风险连续随机变量。对于许多连续随机变量，风险度量等于最坏情况下的风险度量，即该赌博所导致的最大可能损失。我们还扩展了福斯特-哈特风险测度的一般分布和概率空间的动态环境中，我们表明，扩展的措施，避免破产无限重复的赌博。
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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