May 2024
Beginner to intermediate
141 pages
2h 7m
Chinese
Content preview from R语言计量金融初学指南Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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第8章 极值理论
极端损失的风险是金融领域和保险领域中许多风险管理问题的核心。一个极端的市场运动可能代表着某个投资者证券组合的显著下跌风险。未来信用损失的准备金大小必须覆盖发生极端风险时的贷款组合损失。一家银行需要的资本水平必须高到足够吸收极端的操作损失。保险公司需要准备好应付于自然产生或者人为造成的灾难，甚至从未有过的数量级的灾难。
极值理论（Extreme Value Theory，EVT）与极端事件的统计分析有关。这种方法论提供的分布与极端观测一致，同时它的参数形式受到理论的支持。EVT的理论意义弥补了传统估计的不可靠性（由极端事件的稀疏数据所引起）。EVT允许量化极端事件的统计，甚至超越了迄今大多数的极端观测。
EVT在金融和保险中最有用的模型类型是阈值超标的模型。这些模型刻画了所有比较大的观测的分布，这些观测都超过了某个高水平值，因此提供了分布的尾部估计。因为许多风险管理问题都根据分布的尾部来进行公式化，所以这些模型可以直接应用于这类问题。
本章的目的是通过一些真实世界的风险管理应用案例，展示极值理论在金融和保险中可能使用的方法。首先，我们提供了一个EVT中阈值超标模型的理论概览。然后，我们详细解决一个例子，用一个模型拟合火灾损失分布的尾部。我们使用拟合模型为火灾损失计算高分位数（在险价值VaR）和条件分布（Expected Shortfall）。
8.1 理论概览
令随机变量X表示我们需要建模的随机损失，
是它的分布函数。对于一个给定的阈值u，超过阈值Y=X−u的超额损失的分布函数如下。 ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.