Some Topics in Robust Mathematical Finance

稳健数学金融中的一些话题

• 批准号: RGPIN-2018-04179
• 负责人: Gao, Niushan
• 金额: $ 1.68万
• 依托单位: Ryerson University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=679420
• 关键词: Some; Topics; Robust; Mathematical; Finance

Model uncertainty is pervasive in finance and economics, and has been gaining more and more attention in recent years. I propose to study the two fundamental subjects in mathematical finance, Pricing and Risk Measurement, under uncertainty, using the robust approach, which is currently a leading research trend in mathematical finance.******1. Robust pricing theory. The goal is to establish robust versions of the Fundamental Theorem of Asset Pricing (FTAP) and the Superhedging Theorem (ST), which are cornerstones of the classical mathematical pricing theory. Although many efforts have been devoted to this area by various researchers, a relatively comprehensive theory is still to be established.******Goals:***- establish a general version of FTAP and ST in the robust setting;***- systematically investigate capacitary function spaces.******2. Risk measurement under uncertainty. The goal is to study how risk measurement is affected by uncertainty and how to take uncertainty into account in risk measurement. ******Goals:***- study risk measures on capacitary function spaces;***- determine risk aggregation bounds under dependence uncertainty subject to correlation constraint.***********

模型不确定性在金融和经济学上普遍存在，并且近年来一直在引起越来越多的关注。我建议在不确定的情况下使用强大的方法研究数学金融，定价和风险测量的两个基本学科，这是目前数学金融的主要研究趋势。****** 1。强大的定价理论。目的是建立资产定价基本定理（FTAP）和超义定理（ST）的强大版本，这些定理是经典数学定价理论的基石。尽管各种研究人员都为这一领域提供了许多努力，但仍将建立一个相对全面的理论。******目标：*** - 在健壮的环境中建立了FTAP和ST的一般版本； *** - 系统地研究电容器功能空间。不确定性下的风险测量。目的是研究风险测量如何受到不确定性的影响以及如何在风险测量中考虑不确定性。 ******目标：*** - 有关电容性功能空间的研究风险措施； *** - 确定依赖性不确定性下的风险聚集界限，但要受相关性约束。**********************************************************