英文标题：
《Fair Estimation of Capital Risk Allocation》
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作者：
Tomasz R. Bielecki, Igor Cialenco, Marcin Pitera, Thorsten Schmidt
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最新提交年份：
2019
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英文摘要：
  In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit formulae for fair capital allocations in case when the constituents of the risky portfolio are jointly normally distributed. The main focus of the paper is on the problem of approximating fair portfolio allocations in the case of not fully known law of the portfolio constituents. We define and study the concepts of fair allocation estimators and asymptotically fair allocation estimators. A substantial part of our study is devoted to the problem of estimating fair risk allocations for expected shortfall. We study this problem under normality as well as in a nonparametric setup. We derive several estimators, and prove their fairness and/or asymptotic fairness. Last, but not least, we propose two backtesting methodologies that are oriented at assessing the performance of the allocation estimation procedure. The paper closes with a substantial numerical study of the subject.
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中文摘要：
本文提出了一种新的风险资本配置估计方法。该方法基于风险度量理论。我们在一个通用但易处理的法律不变一致风险度量类别内工作，特别关注预期缺口。我们引入了公平资本分配的概念，并在风险投资组合的组成部分为联合正态分布的情况下，提供了公平资本分配的明确公式。本文的主要重点是在投资组合组成部分的规律不完全已知的情况下，近似公平的投资组合分配问题。定义并研究了公平分配估计量和渐近公平分配估计量的概念。我们研究的很大一部分致力于估计预期缺口的公平风险分配问题。我们在正态和非参数条件下研究这个问题。我们推导了几个估计量，并证明了它们的公平性和/或渐近公平性。最后，但并非最不重要的是，我们提出了两种回溯测试方法，旨在评估分配估计过程的性能。本文最后对这一主题进行了大量的数值研究。
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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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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
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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