Systemic Risk and Nonlinear Problems in Financial Mathematics

金融数学中的系统性风险和非线性问题

• 批准号: 1409434
• 负责人: Jean-Pierre Fouque
• 金额: $ 38.3万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1409434&HistoricalAwards=false
• 关键词: Systemic; Risk; Nonlinear; Problems; Financial

FouqueDMS-1409434 Challenging nonlinear problems arising naturally in the context of risk management under uncertain or randomly fluctuating volatility and under liquidity constraints are addressed in the first part of the project. This work has direct applications to problems faced by practitioners in the financial industry, including pension funds managers. The second part of the project is a study of systemic risk and mathematical analysis of the stability (or instability) of our banking system. The recent financial crisis has revealed a lack of understanding of the risk of cascade of defaults in banking networks. To help assess measures of such systemic risks, the investigator develops and analyzes new stochastic games models of borrowing and lending among banks. A graduate student and a postdoctoral researcher are engaged in the project each year. This project, including its training component, contributes to the effort started by the regulators in the recent creation of the Office of Financial Research. In the first part of the project, the investigator establishes new results in the theory of asymptotic analysis and homogenization of nonlinear partial partial differential equations, with direct applications to several important and practical problems in financial mathematics. These problems include risk management under uncertain volatility, portfolio optimization under stochastic volatility, and investment with co-integrated assets. In the second part of the project, he studies stochastic games models of inter-bank borrowing and lending with applications to measures of systemic risk. New mathematical problems arise naturally; they include backward-forward stochastic partial differential equations and stochastic games with delay. A graduate student and a postdoctoral researcher are engaged in the project each year.

FouqueDMS-1409434 在不确定或随机波动的波动率和流动性约束下的风险管理的背景下自然产生的非线性问题，解决在该项目的第一部分。 这项工作直接应用于金融业从业人员面临的问题，包括养老基金经理。 第二部分是系统性风险的研究和对我国银行体系稳定性（或不稳定性）的数学分析。 最近的金融危机表明，人们对银行网络中一连串违约的风险缺乏了解。 为了帮助评估这种系统性风险的措施，调查员开发和分析新的银行间借贷的随机博弈模型。 每年有一名研究生和一名博士后研究人员从事该项目。 该项目，包括其培训部分，有助于监管机构最近在设立金融研究办公室方面开始的努力。 在项目的第一部分，研究者建立了非线性偏微分方程的渐近分析和均匀化理论的新结果，并直接应用于金融数学中的几个重要和实际问题。 这些问题包括不确定波动率下的风险管理、随机波动率下的投资组合优化以及协整资产下的投资问题。 在项目的第二部分，他研究了银行间借贷的随机博弈模型，并将其应用于系统风险的度量。 新的数学问题自然出现，它们包括向后-向前随机偏微分方程和随机游戏延迟。 每年有一名研究生和一名博士后研究人员从事该项目。