Robust Methods in Mathematical Finance

数学金融中的稳健方法

• 批准号: 1515753
• 负责人: Rene Carmona
• 金额: $ 23.72万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1515753&HistoricalAwards=false
• 关键词: Robust; Methods; Mathematical; Finance

Stochastic models have long been successfully applied to describe financial markets, make investment decisions, price and hedge financial derivatives, and manage risks. But this has led to an over-reliance on particular models and a disregard of the possibility of model misspecification. While in most engineering applications robust methods have a long history, the standard approach in mathematical finance is still to describe all underlying uncertainty with a single probability measure. However, in many real-life situations it is not possible to determine the precise probabilities of future events, and financial decision rules that are sensitive to particular assumptions can lead to disastrous outcomes if reality does not exactly unfold as predicted by the model. The goal of this project is to develop methods of financial decision-making that take into account extreme events and are robust with respect to model misspecification. The outcomes are expected to lead to robust approaches to investing, asset pricing, hedging, and risk management. Graduate students are included in the work of the project. The project aims to create robust methods that can be used to address relevant problems in mathematical finance. Discrete-time as well as continuous-time models are studied. The plan is to establish non-linear Riesz representation results that can be used to develop robust versions of the fundamental theorem of asset pricing together with corresponding pricing duality formulas, robust methods for pricing and hedging options, as well as approaches to treat optimal asset allocation problems under model uncertainty. The problems to be addressed lie at the intersection of mathematical finance, investment theory, and financial economics. Methods from probability theory, stochastic analysis, functional analysis, and decision theory are used.

随机模型长期以来一直成功应用于描述金融市场、做出投资决策、定价和对冲金融衍生品以及管理风险。 但这导致了对特定模型的过度依赖，并且忽视了模型错误指定的可能性。 虽然在大多数工程应用中稳健的方法有着悠久的历史，但数学金融中的标准方法仍然是用单一概率度量来描述所有潜在的不确定性。 然而，在许多现实生活中，不可能确定未来事件的精确概率，如果现实没有完全按照模型预测的那样展开，对特定假设敏感的财务决策规则可能会导致灾难性的结果。 该项目的目标是开发考虑极端事件并且在模型错误指定方面稳健的财务决策方法。 预计研究结果将带来稳健的投资、资产定价、对冲和风险管理方法。 研究生参与该项目的工作。该项目旨在创建可用于解决数学金融相关问题的稳健方法。 研究了离散时间和连续时间模型。 该计划是建立非线性 Riesz 表示结果，可用于开发资产定价基本定理的稳健版本以及相应的定价对偶公式、稳健的定价方法和对冲期权，以及处理最优资产配置的方法模型不确定性下的问题。 要解决的问题位于数学金融、投资理论和金融经济学的交叉点。 使用概率论、随机分析、泛函分析和决策论的方法。