英文标题：
《Tail behavior of sums and differences of log-normal random variables》
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作者：
Archil Gulisashvili, Peter Tankov
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最新提交年份：
2016
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英文摘要：
  We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior turns out to depend on the correlation between the components, and the explicit solution is found by solving a tractable quadratic optimization problem. These results can be used either to approximate the probability of tail events directly, or to construct variance reduction procedures to estimate these probabilities by Monte Carlo methods. In particular, we propose an efficient importance sampling estimator for the left tail of the distribution function of the sum of log-normal variables. As a corollary of the tail asymptotics, we compute the asymptotics of the conditional law of a Gaussian random vector given a linear combination of exponentials of its components. In risk management applications, this finding can be used for the systematic construction of stress tests, which the financial institutions are required to conduct by the regulators. We also characterize the asymptotic behavior of the Value at Risk for log-normal portfolios in the case where the confidence level tends to one.
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中文摘要：
我们给出了相关对数正态随机变量线性组合的密度和分布函数的尖尾渐近性，即相关高斯向量分量的指数。渐近行为取决于各分量之间的相关性，显式解是通过求解一个可处理的二次优化问题得到的。这些结果既可以直接用来近似尾部事件的概率，也可以用来构造方差缩减程序，用蒙特卡罗方法估计这些概率。特别地，我们对对数正态变量和的分布函数的左尾提出了一个有效的重要抽样估计。作为尾部渐近性的一个推论，我们计算高斯随机向量的条件律的渐近性，给定其分量的指数的线性组合。在风险管理应用中，这一发现可用于系统构建压力测试，监管机构要求金融机构进行压力测试。在置信水平趋于1的情况下，我们还刻画了对数正态投资组合的风险价值的渐近行为。
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分类信息：

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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