Collaborative Research: High-Performance Computational Methods for Continuous-Time Markov Processes in Financial Engineering

合作研究：金融工程中连续时间马尔可夫过程的高性能计算方法

• 批准号: 0422937
• 负责人: Vadim Linetsky
• 金额: $ 27.96万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-10-01 至 2008-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0422937&HistoricalAwards=false
• 关键词: Collaborative; Research; Performance; Computational; Methods

This grant provides funding for the development of high-performance computational tools for financial engineering. The goal is to develop computational methods to evaluate complex financial products used to manage foreign exchange, interest rate, equity, commodity, energy, and credit risks, manage portfolios of assets, and evaluate financial contracts and equipment leases in manufacturing industries. The methodology is based on the extension to financial engineering of finite element methods used to solve numerically partial differential equations. Partial integro-differential equations arise in Markov jump-diffusion models, associated optimal stopping, and stochastic control problems in financial engineering. Finite element methods will be applied to jump-diffusion processes to develop computational tools to be used by practitioners in the financial services industry, as well as researchers in financial engineering, applied probability, and operations research. Applications include pricing algorithms for a wide range of financial contracts (equity and foreign exchange options, interest rate derivatives, commodity contracts, and equipment leases in manufacturing), as well as portfolio optimization with transaction costs and trading restrictions.If successful, methodologies developed in this project will help financial institutions, corporate treasuries of manufacturing and service firms, and energy companies accurately value complex financial instruments and efficiently manage financial risks. This project will also have a broader impact on research and application areas that use continuous-time Markov processes, such as heavy traffic limits in queuing theory, inventory control, scheduling, and manufacturing. The results on constructive approximations to the valuation, optimal stopping and stochastic control problems will also help simulation and stochastic optimization research by providing reliable benchmarks for simulation and stochastic optimization. This grant supports the Ph.D. concentration in financial engineering at Northwestern. This will result in training highlyqualified researchers in financial engineering for academia and industry. The grant will also help the Department of Mathematical Sciences at the University of Nevada establish a research program in financial mathematics.

这笔赠款为金融工程高性能计算工具的开发提供资金。目标是开发计算方法来评估复杂的金融产品，用于管理外汇、利率、股票、商品、能源和信用风险，管理资产组合，以及评估制造业的金融合同和设备租赁。该方法基于用于求解数值偏微分方程的有限元方法向金融工程的扩展。偏积分微分方程出现在马尔可夫跳跃扩散模型、相关的最优停止和金融工程中的随机控制问题中。有限元方法将应用于跳跃扩散过程，以开发供金融服务行业从业者以及金融工程、应用概率和运筹学研究人员使用的计算工具。应用包括各种金融合约（股票和外汇期权、利率衍生品、商品合约和制造业设备租赁）的定价算法，以及交易成本和交易限制的投资组合优化。如果成功，方法论将在该项目将帮助金融机构、制造和服务公司的企业金库以及能源公司准确评估复杂的金融工具并有效管理金融风险。该项目还将对使用连续时间马尔可夫过程的研究和应用领域产生更广泛的影响，例如排队论、库存控制、调度和制造中的大流量限制。评估、最优停止和随机控制问题的建设性近似结果也将通过为模拟和随机优化提供可靠的基准来帮助模拟和随机优化研究。这笔赠款支持博士学位。西北大学的金融工程专业。这将为学术界和工业界培训高素质的金融工程研究人员。这笔赠款还将帮助内华达大学数学科学系建立金融数学研究项目。