Stochastic Modelling and Control in High Frequency Finance

高频金融中的随机建模和控制

• 批准号: 261799-2013
• 负责人: Jaimungal, Sebastian
• 金额: $ 1.68万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635750
• 关键词: Stochastic; Modelling; Control; Frequency; Finance

Today most trading in equity markets takes place on competing electronic platforms typically run by exchanges or large brokers. This changing trading environment has opened a host of new mathematical and statistical modeling problems at the cutting edge of mathematical finance research. My research program aims to address the mathematical and statistical aspects of high frequency trading (HFT) and algorithmic trading (AT) and focuses on two main areas: (i) Stochastic Control problems related to HFT and AT and (ii) Statistical modeling and machine learning (ML) in limit order books (LOBs).The first aspect deals with the posing and solving of stochastic optimal control and stopping problems including optimal liquidation (OL) and optimal market-making (MM) problems. Building a sound understanding of these problems is important from a regulation point of view as well as for institutional investors to manage their liquidity risks better. The second area is data driven and focuses on the statistical modeling of high frequency (HF) financial data. Building realistic statistical models is the key for developing continuous time stochastic models of HF markets and in developing our understanding of market microstructure.The mathematical and statistic modeling problems that this research program addresses will have a wide impact. Regulators will be able to use the developments to assess the impact that various policies will have on markets and to assess how HF trading affects slower traders. Moreover, the research outputs will be applicable to fields as diverse as biostatistics (latent models of event data), economics and insurance (ambiguity aversion on PRMs), and mathematics (duality methods for PRMs). Finally, I anticipate that the tools I develop will be adopted by industry practitioners to create robust and efficient trading strategies.

如今，股票市场上的大多数交易都是在竞争性的电子平台上进行的，通常由交易所或大型经纪人运行。这种不断变化的交易环境为数学金融研究的最前沿开辟了许多新的数学和统计建模问题。 My research program aims to address the mathematical and statistical aspects of high frequency trading (HFT) and algorithmic trading (AT) and focuses on two main areas: (i) Stochastic Control problems related to HFT and AT and (ii) Statistical modeling and machine learning (ML) in limit order books (LOBs).The first aspect deals with the posing and solving of stochastic optimal control and stopping problems including optimal liquidation (OL) and optimal营销（MM）问题。从法规的角度以及机构投资者以更好地管理其流动性风险，对这些问题有合理的了解至关重要。第二个领域是数据驱动的，并着重于高频（HF）财务数据的统计建模。建立现实的统计模型是开发HF市场连续时间随机模型以及发展我们对市场微观结构的理解的关键。该研究计划解决的数学和统计建模问题将产生广泛的影响。监管机构将能够利用这些发展来评估各种政策对市场的影响，并评估HF交易如何影响较慢的交易者。此外，研究输出将适用于与生物统计学（事件数据的潜在模型），经济学和保险（PRMS的歧义性厌恶）和数学（PRMS的双重性方法）等多样化的领域。最后，我预计我开发的工具将被行业从业人员采用，以创建强大而有效的交易策略。