英文标题：
《Stochastic PDEs for large portfolios with general mean-reverting
volatility processes》
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作者：
Ben Hambly and Nikolaos Kolliopoulos
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最新提交年份：
2021
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英文摘要：
In this article we consider a structural stochastic volatility model for the loss from a large portfolio. Both the asset value and the volatility processes are correlated through systemic Brownian motions, and the second ones are picked from a class of general mean-reverting diffusions. We prove that our system converges as the portfolio becomes large and, when the vol-of-vol function satisfies certain regularity and boundedness conditions, the limit of the empirical measure process has a density given in terms of a solution to a stochastic initial-boundary value problem on a half-space. The problem is defined in a special weighted Sobolev space. A good regularity result is established for solutions to this problem, and then we show that there exists a unique solution. In contrast to the CIR volatility setting covered by the existing literature, our results hold even when the systemic Brownian motions are taken to be correlated.
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中文摘要：
在本文中，我们考虑一个大型投资组合损失的结构随机波动率模型。资产价值和波动过程都通过系统布朗运动进行关联，第二个过程从一类广义均值回复扩散中选龋我们证明了当投资组合变大时，我们的系统收敛，并且当vol-of-vol函数满足一定的正则性和有界性条件时，经验测度过程的极限有一个密度，该密度由半空间上随机初边值问题的解给出。该问题定义在一个特殊的加权Sobolev空间中。对该问题的解建立了一个很好的正则性结果，并证明了存在唯一解。与现有文献中涵盖的CIR波动率设置相反，即使系统布朗运动被认为是相关的，我们的结果仍然成立。
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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：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE\'s, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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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：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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