Topics in Mathematical Finance and Stochastic Control

数学金融与随机控制专题

• 批准号: 0604643
• 负责人: Mihai Sirbu
• 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: 2006
• 资助国家: 美国
• 起止时间: 2006-07-15 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604643&HistoricalAwards=false
• 关键词: Topics; Mathematical; Finance; Stochastic; Control

In this project, the two-times differentiability of the value functions in the problem of optimal investment in incomplete markets and the sensitivity analysis of utility-based prices for the case of utility functions defined on the whole real line is considered. The research focuses on necessary and sufficient conditions under which the mathematical statements hold. In particular, we are looking for the largest class of contingent claims that can be analyzed in this framework. The risk-tolerance wealth process turns out to be the appropriate numeraire for pricing. In addition, a class of multi-dimensional stochastic games is studied.In complete markets, described by models like the Black and Scholes model, prices are uniquely defined by "no-arbitrage" considerations. In more realistic models, which are incomplete, prices of contingent claims can only be defined taking into account the preferences and wealth of specific investors. The dependence of prices on the number of contingent claims for investors who can borrow any amount of cash from the money market (infinite credit line) is studied. The pricing techniques can be applied to a large number of incomplete models, including options on non-traded assets and energy derivatives.

在这个项目中，考虑了在不完整市场的最佳投资问题中的价值功能的两次不同性能以及对整个真实行中定义的实用程序功能的基于公用事业价格的敏感性分析。 该研究集中在数学陈述所持的必要条件下。特别是，我们正在寻找可以在此框架中分析的最大一类的特征主张。 事实证明，承受风险的财富过程是定价的合适数字。此外，还研究了一类多维随机游戏。在完整的市场中，由黑色和斯科尔斯模型等模型描述，价格由“无竞技”的注意事项唯一地定义。在不完整的更现实的模型中，只有考虑到特定投资者的偏好和财富才能定义或有索赔的价格。 研究了可以从货币市场（无限信用额度）借用任何数量现金的投资者的价格依赖性。 定价技术可以应用于大量不完整的模型，包括非交易资产和能源衍生品的选项。