Optimal Control of Stochastic Partial Differential Equations

随机偏微分方程的最优控制

• 批准号: DP0346406
• 负责人: Prof Beniamin Goldys
• 金额: $ 3.41万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-07 至 2005-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0346406
• 关键词: Optimal; Control; Stochastic; Partial; Differential

The problem to control a stochastic process so as to minimize a certain cost functional arises in many areas of Applied Sciences, Engineering and Mathematical Finance. An important practical question is to find, for a given cost functional, the optimizing control in a feedback form. We propose new tools to construct such optimal controls for a class of stochastic processes which are solutions to stochastic partial differential equations. As an outcome of this project we will obtain methods to determine the optimal control policies for a large variety of cost functionals and degenerated stochastic partial differential equations, in particular those arising in modelling of volatility in Finance.

控制一个随机过程以使某个成本泛函最小化的问题在应用科学、工程和金融数学的许多领域都有出现。一个重要的实际问题是，对于给定的成本泛函，找到反馈形式的最优控制。我们提出了新的工具来构造这样的最优控制一类随机过程的随机偏微分方程的解决方案。作为这个项目的结果，我们将获得的方法来确定各种各样的成本泛函和退化的随机偏微分方程，特别是在金融波动建模中产生的最优控制策略。