Stochastic Representation Problems for Optimal Control and Nonlinear Models for Illiquid Financial Markets

非流动性金融市场最优控制的随机表示问题和非线性模型

• 批准号: 0505021
• 负责人: Peter Bank
• 金额: $ 11.29万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505021&HistoricalAwards=false
• 关键词: Stochastic; Representation; Problems; Optimal; Control

The project focuses on novel approaches to stochastic optimization problems arising in Mathematical Finance and Economics. A key topic is the development and analysis of new mathematical models for illiquid financial markets which account for the dependence between asset price dynamics and trading strategies, leading to new applications for the nonlinear stochastic integration theory developed by Kunita and Carmona/Nualart in the 1990s. Furthermore, we will develop new analytic and numerical methods to both one- and two-sided singular control problems, building on their relation to certain representations of stochastic processes.The vast majority of models presently studied in Mathematical Finance specify asset price dynamics as an exogenously given process, which evolves independently from the trading strategies employed by the market participants. While this idealization is appropriate for liquid markets (trading, for instance, treasury bonds or blue chips), it is largely open at present how to assess the liquidity risk in markets where asset prices are directly related to the demand generated by traders. The development and analysis of mathematical models capturing this nonlinear feedback affect between prices and trading strategies poses a challenge for stochastic optimization and control that is addressed by this project.

该项目重点研究数学金融与经济学中出现的随机优化问题的新方法。一个关键主题是开发和分析非流动性金融市场的新数学模型，该模型解释了资产价格动态和交易策略之间的依赖关系，从而为Kunita和Carmona/Nualart在20世纪90年代开发的非线性随机积分理论提供了新的应用。此外，我们将开发新的解析和数值方法来解决单边和双边奇异控制问题，建立在它们与随机过程的某些表示的关系之上。目前在数学金融中研究的绝大多数模型都将资产价格动态指定为一个外生给定过程，该过程独立于市场参与者所采用的交易策略而发展。虽然这种理想化适用于流动性市场（例如，交易国库券或蓝筹股），但目前如何评估资产价格与交易者产生的需求直接相关的市场的流动性风险在很大程度上是开放的。数学模型的开发和分析捕捉了价格和交易策略之间的非线性反馈影响，这对该项目所解决的随机优化和控制提出了挑战。