论文标题
最大货币风险措施：最坏的风险评估和急剧的大偏差
Maxitive monetary risk measures: worst-case risk assessment and sharp large deviations
论文作者
论文摘要
在不确定性和风险下的决策中，最坏的风险评估通常是使用最大货币风险措施进行的。在本文中，我们研究了所有随机变量的空间上的最大货币风险度量，几乎可以肯定的平等。我们证明，货币风险措施从下面且仅当它是受惩罚的最大损失时，是最大且连续的。此外，我们将最大损失描述为独特的最大和法律不变的货币风险度量。我们通过提供一个通用标准来建立概率度量序列的急剧大偏差估计，将结果应用于大偏差理论。我们使用这些发现为风险汇集的扭曲指数保险费原则的渐近学提供了公式。
In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables identified modulo almost sure equality. We prove that a monetary risk measure is maxitive and continuous from below if and only if it is a penalized maximum loss. Furthermore, we characterize the maximum loss as the unique maxitive and law-invariant monetary risk measure. We apply the results to large deviation theory by providing a general criterion to establish a sharp large deviation estimate for sequences of probability measures. We use these findings to provide a formula for the asymptotics of the distortion-exponential insurance premium principle under risk pooling.
