英文标题：
《Law invariant risk measures and information divergences》
---
作者：
Daniel Lacker
---
最新提交年份：
2016
---
英文摘要：
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences include many classical information divergence measures, such as relative entropy and $f$-divergences. Several properties of divergence and their duality with law invariant risk measures are developed, most notably relating their chain rules or additivity properties with certain notions of time consistency for dynamic law invariant risk measures known as acceptance and rejection consistency. These properties are linked also to a peculiar property of the acceptance sets on the level of distributions, analogous to results of Weber on weak acceptance and rejection consistency. Finally, the examples of shortfall risk measures and optimized certainty equivalents are discussed in some detail, and it is shown that the relative entropy is essentially the only divergence satisfying the chain rule.
---
中文摘要：
在律不变风险测度和发散之间建立了一一对应关系，我们将其定义为满足一些自然性质的任意标准Borel空间上概率测度对的泛函。发散包括许多经典的信息发散度量，如相对熵和$f$发散。发展了散度的若干性质及其与律不变风险度量的对偶性，最显著的是将其链式规则或可加性性质与动态律不变风险度量的某些时间一致性概念（称为接受和拒绝一致性）联系起来。这些性质还与分布水平上接受集的一个特殊性质有关，类似于韦伯关于弱接受和拒绝一致性的结果。最后，详细讨论了短缺风险度量和优化确定性等价物的例子，结果表明，相对熵本质上是满足链式规则的唯一散度。
---
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
--
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--

---
PDF下载：
-->