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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712768
• 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.

模型不确定性是金融经济学中普遍存在的问题，近年来受到越来越多的关注。我建议研究两个基本的问题，在数学金融，定价和风险度量，在不确定性下，使用鲁棒方法，这是目前在数学金融的主要研究趋势。 1.稳健定价理论目标是建立资产定价基本定理（FTAP）和超对冲定理（ST）的稳健版本，这是经典数学定价理论的基石。虽然许多研究者在这方面做了大量的工作，但一个相对完整的理论仍有待建立。 目标： - 在稳健环境中建立FTAP和ST的通用版本; - 系统地研究了容性函数空间。 2.不确定性下的风险度量。研究不确定性对风险度量的影响以及如何在风险度量中考虑不确定性。 目标： - 研究容性函数空间上的风险度量; - 在相关性约束下确定相关不确定性下的风险聚集边界。