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地用于描述金融市场，做出投资决策，价格和对冲金融衍生品并管理风险。 但这导致了对特定模型的过度依赖，并且无视模型错误的可能性。 尽管在大多数工程应用中，鲁棒方法具有较长的历史，但数学金融的标准方法仍然是用单个概率度量来描述所有潜在的不确定性。 但是，在许多现实生活中，不可能确定未来事件的确切概率，如果现实并没有像模型所预测的那样完全展现，那么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。 该项目的目的是开发财务决策的方法，这些方法考虑到极端事件，并且在模型错误指定方面是强大的。 预计结果将导致强大的投资，资产定价，对冲和风险管理的方法。 研究生被包括在项目的工作中。该项目旨在创建可用于解决数学金融中相关问题的强大方法。 研究了离散的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强大版本，以及相应的定价二重性公式，适合定价和套期选择的强大方法，以及在模型不确定下处理最佳资产分配问题的方法。 要解决的问题在于数学金融，投资理论和金融经济学的交集。 使用了概率理论，随机分析，功能分析和决策理论的方法。