"Non Probabilistic Financial Mathematics. Discretization of Processes, Wavelets and Applications."

“非概率金融数学。过程、小波和应用的离散化。”

• 批准号: 194624-2012
• 负责人: Ferrando, Sebastian
• 金额: $ 0.87万
• 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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635596
• 关键词: Non; Probabilistic; Financial; Mathematics.; Discretization

The proposal introduces innovative ideas, concepts and techniques that contribute to the theory of modern financial mathematics and the use of signal processing methods in probabilistic settings.The application areas are arbitrage, hedging and pricing in financial mathematics as well as some topics from image processing and nonlinear regression of hedge funds. Arbitrage refers to the possibility of making a profit without risk and hedging, in broad terms, means the re-adjustment of portfolio positions to meet future financial obligations. These key foundational concepts are used to build mathematical marketmodels; in particular, they provide the derived notion of price for financial instruments. One of our research projects describes a new non probabilistic approach to the foundational notions of arbitrage, hedging and pricing, the approach emphasizes questions of the type: what are the properties of an unfolding stock chart for a financial stock? This question is dealt with without considering the probability that the path may have in a certain stochastic model. The proposed point of view carries empirical implications for the possible range of prices of financial products as well as risk analysis. Some of these implications will be developed in the proposed research.Another research project develops new mathematical tools for image and video processing as well as cell recognition in two and three dimensional images. This project leads to advances in technological innovations, a main goal is to implement these new algorithms in software that will be made available to the research community. A related project proposes to make use of the new signal processing methodology of compressed sensing in a financial context in order to estimate the behavior of a portfolio in the presence of scarce observations. The methodology offers several potential advantages as it accounts for the joint probability of risk factors.

该提案介绍了有助于现代金融数学理论和概率环境中信号处理方法使用的创新思想、概念和技术。应用领域包括金融数学中的套利、对冲和定价，以及对冲基金的图像处理和非线性回归的一些主题。套利是指在没有风险的情况下获利的可能性，而对冲从广义上讲是指重新调整投资组合头寸以满足未来的财务义务。这些关键的基本概念用于构建数学市场模型；特别是，它们提供了金融工具价格的衍生概念。我们的一个研究项目描述了一种新的非概率方法来处理套利、对冲和定价的基本概念，该方法强调以下类型的问题：金融股票的展开股票图表的属性是什么？处理这个问题时没有考虑路径在某个随机模型中可能具有的概率。所提出的观点对金融产品的可能价格范围以及风险分析具有实证意义。其中一些影响将在拟议的研究中得到发展。另一个研究项目开发用于图像和视频处理以及二维和三维图像中的细胞识别的新数学工具。该项目带来了技术创新的进步，主要目标是在软件中实现这些新算法，供研究界使用。一个相关项目建议在金融背景下利用压缩感知的新信号处理方法，以便在存在稀缺观察的情况下估计投资组合的行为。该方法提供了几个潜在的优势，因为它考虑了风险因素的联合概率。