"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以及在概率环境中使用信号处理方法的创新思想，概念和技术。应用领域是套利，金融数学以及图像处理和图像处理和图像处理和图像处理和图像处理和图像处理和一些主题的应用领域对冲基金的非线性回归。套利是指从没有风险和对冲的情况下赚取利润的可能性，这意味着重新调整投资组合职位以履行未来的财务义务。这些关键的基础概念用于构建数学市场建模。特别是，它们提供了金融工具的价格概念。我们的研究项目之一描述了一种针对套利，对冲和定价的基础概念的一种新的非概率方法，该方法强调了这种类型的问题：金融股票的不断发展的股票图表的特性是什么？解决这个问题的情况下，没有考虑该路径在某个随机模型中可能具有的概率。拟议的观点对金融产品价格的可能范围以及风险分析具有经验意义。其中一些含义将在拟议的研究中开发出来。其他研究项目开发了用于图像和视频处理的新数学工具，以及两个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施这些新算法，这些算法将提供给研究社区。一个相关项目建议在财务环境中使用新的信号处理方法，以估计在缺乏观察的情况下投资组合的行为。该方法提供了几种潜在的优势，因为它说明了危险因素的共同可能性。