英文标题：
《Fast mean-reversion asymptotics for large portfolios of stochastic
  volatility models》
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作者：
Ben Hambly and Nikolaos Kolliopoulos
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最新提交年份：
2020
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英文摘要：
  We consider an SPDE description of a large portfolio limit model where the underlying asset prices evolve according to certain stochastic volatility models with default upon hitting a lower barrier. The asset prices and their volatilities are correlated via systemic Brownian motions, and the resulting SPDE is defined on the positive half-space with Dirichlet boundary conditions. We study the convergence of the loss from the system, a function of the total mass of a solution to this stochastic initial-boundary value problem under fast mean reversion of the volatility. We consider two cases. In the first case the volatility converges to a limiting distribution and the convergence of the system is in the sense of weak convergence. On the other hand, when only the mean reversion of the volatility goes to infinity we see a stronger form of convergence of the system to its limit. Our results show that in a fast mean-reverting volatility environment we can accurately estimate the distribution of the loss from a large portfolio by using an approximate constant volatility model which is easier to handle.
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中文摘要：
我们考虑了一个大型投资组合限额模型的SPDE描述，其中标的资产价格根据一定的随机波动率模型演化，当达到较低的障碍时会发生违约。资产价格及其波动率通过系统布朗运动进行关联，并在Dirichlet边界条件下的正半空间上定义了由此产生的SPDE。我们研究了在波动率快速均值回复下，系统损失的收敛性，这是一个随机初边值问题解的总质量的函数。我们考虑两种情况。在第一种情况下，波动率收敛到极限分布，系统的收敛是弱收敛的。另一方面，当波动率只有均值回归到无穷大时，我们看到系统收敛到极限的形式更强。我们的结果表明，在快速均值回复波动率环境中，我们可以通过使用更容易处理的近似常数波动率模型准确估计大型投资组合的损失分布。
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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：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：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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