Mathematical Sciences: Stochastic Control and Applications in Mathematical Economics

数学科学：随机控制及其在数理经济学中的应用

• 批准号: 8723078
• 负责人: Ioannis Karatzas
• 金额: $ 16.27万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8723078&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stochastic; Control; Applications

Research in stochastic analysis and control, with special emphasis on mathematical economics and on problems of singular control and optimal stopping. Particular topics include: (i) a detailed study of single-agent portfolio/consumption problems with very general market models and utility functions, using techniques from stochastic analysis; (ii) the associated treatment of equilibrium problems for an economy with several agents, whose joint optimal actions determine the prices of traded commodites by "clearing" the markets; (iii) a new approach to optimal stopping using the theory of balayage semimartingales, and the discussion of its ramifications for the reflection problem of Skorohod and for singular stochastic control; and (iv) a study of integral functionals for diffusion processes and semimartingales.

研究随机分析和控制，特别强调数学经济学和奇异控制和最优停止问题。具体的主题包括：(I)使用随机分析的技术，用非常一般的市场模型和效用函数详细研究单代理投资组合/消费问题；(2)对有多个代理人的经济体的均衡问题的相关处理，这些代理人的联合最优行动通过“清算”市场来决定交易商品的价格；(3)利用平衡态半鞅理论给出了最优停止的一种新方法，并讨论了它对Skorohod反射问题和奇异随机控制的影响；以及(Iv)扩散过程和半鞅的积分泛函的研究。