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摘要翻译：
风险价值（VaR）和条件风险价值（CVaR）是风险管理实践中广泛应用的两种风险度量方法。本文讨论了用随机逼近（递减步骤）计算VaR和CVaR的问题：我们提出了基于Rockaffelar-Uryasev恒等式的CVaR的第一个Robbins-Monro过程。该算法对目标的收敛速度满足一个高斯中心极限定理。作为第二步，为了加快初始过程，我们提出了一种递归重要性抽样（I.S.）使VaR和CVaR的方差显著降低。这一思想可以追溯到B.Arouna的开创性论文，遵循了V.Lemaire和G.Pag\'es引入的新方法。最后，我们考虑了一个确定性的移动风险水平来加快算法的初始化阶段。我们证明了该方法的收敛速度服从一个具有最小方差的中心极限定理，并通过考虑几个典型的能量组合来说明其有效性。
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英文标题：
《Computation of VaR and CVaR using stochastic approximations and
unconstrained importance sampling》
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作者：
Olivier Aj Bardou (PMA, GDF-RDD), Noufel Frikha (PMA, GDF-RDD), G.
Pag\`es (PMA)
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最新提交年份：
2010
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分类信息：
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：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：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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英文摘要：
Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) are two risk measures which are widely used in the practice of risk management. This paper deals with the problem of computing both VaR and CVaR using stochastic approximation (with decreasing steps): we propose a first Robbins-Monro procedure based on Rockaffelar-Uryasev's identity for the CVaR. The convergence rate of this algorithm to its target satisfies a Gaussian Central Limit Theorem. As a second step, in order to speed up the initial procedure, we propose a recursive importance sampling (I.S.) procedure which induces a significant variance reduction of both VaR and CVaR procedures. This idea, which goes back to the seminal paper of B. Arouna, follows a new approach introduced by V. Lemaire and G. Pag\`es. Finally, we consider a deterministic moving risk level to speed up the initialization phase of the algorithm. We prove that the convergence rate of the resulting procedure is ruled by a Central Limit Theorem with minimal variance and its efficiency is illustrated by considering several typical energy portfolios.
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PDF链接：
https://arxiv.org/pdf/0812.3381
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