"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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569808
• 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 market models; 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.

该提案介绍了创新的想法，概念和技术，有助于现代金融数学理论和概率环境中信号处理方法的使用。 其应用领域包括金融数学中的套利、套期保值和定价，以及图像处理和对冲基金的非线性回归等。 套利是指在没有风险的情况下获利的可能性，而对冲，广义上说，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建立数学市场 模型;特别是，它们提供了衍生的金融工具价格概念。我们的一个研究项目描述了一种新的非概率方法的基本概念的套利，对冲和定价，该方法强调的问题的类型：什么是一个金融股票的展开股票图表的属性？这个问题的处理没有考虑的概率，路径可能有一定的随机模型。 本文的观点对金融产品的可能价格范围和风险分析具有实证意义。其中一些影响将在拟议的研究中开发。 另一个研究项目是开发新的数学工具，用于图像和视频处理以及二维和三维图像中的细胞识别。该项目导致技术创新的进步，主要目标是在软件中实现这些新算法，这些新算法将提供给研究界。一个相关的项目提出了利用新的信号处理方法的压缩传感在金融方面，以估计的行为的投资组合中存在的稀缺观测。该方法提供了几个潜在的优势，因为它考虑到了风险因素的联合概率。