英文标题：
《Estimation of Risk Contributions with MCMC》
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作者：
Takaaki Koike, Mihoko Minami
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最新提交年份：
2019
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英文摘要：
Determining risk contributions of unit exposures to portfolio-wide economic capital is an important task in financial risk management. Computing risk contributions involves difficulties caused by rare-event simulations. In this study, we address the problem of estimating risk contributions when the total risk is measured by value-at-risk (VaR). Our proposed estimator of VaR contributions is based on the Metropolis-Hasting (MH) algorithm, which is one of the most prevalent Markov chain Monte Carlo (MCMC) methods. Unlike existing estimators, our MH-based estimator consists of samples from conditional loss distribution given a rare event of interest. This feature enhances sample efficiency compared with the crude Monte Carlo method. Moreover, our method has the consistency and asymptotic normality, and is widely applicable to various risk models having joint loss density. Our numerical experiments based on simulation and real-world data demonstrate that in various risk models, even those having high-dimensional (approximately 500) inhomogeneous margins, our MH estimator has smaller bias and mean squared error compared with existing estimators.
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中文摘要：
确定单位风险敞口对整个投资组合经济资本的风险贡献是金融风险管理中的一项重要任务。计算风险贡献涉及罕见事件模拟造成的困难。在这项研究中，我们解决了当总风险由风险价值（VaR）衡量时，估计风险贡献的问题。我们提出的VaR贡献估计基于Metropolis-Hasting（MH）算法，该算法是最流行的马尔可夫链蒙特卡罗（MCMC）方法之一。与现有估计不同，我们基于MH的估计由给定罕见事件的条件损失分布的样本组成。与原始蒙特卡罗方法相比，该特征提高了样本效率。此外，我们的方法具有一致性和渐近正态性，广泛适用于具有联合损失密度的各种风险模型。我们基于模拟和真实数据的数值实验表明，在各种风险模型中，即使是那些具有高维（约500）不均匀裕度的模型，我们的MH估计量与现有估计量相比具有更小的偏差和均方误差。
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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：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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