Inhomogeneous Random Evolutions and their Applications in Finance

非齐次随机演化及其在金融中的应用

• 批准号: RGPIN-2015-04644
• 负责人: Swishchuk, Anatoliy
• 金额: $ 1.24万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=666304
• 关键词: Inhomogeneous; Random; Evolutions; their; Applications

A random evolution, in physical language, is a model for a dynamical system in random environment, whose equation of state is subject to random variations; for example, a stock/asset that switches between different volatilities. In mathematical language, a random evolution is a product of semi-group of operators (describing the evolution of the system) driven by some stochastic process. The stochastic process defines the name for the random evolutions: Markov, semi-Markov, etc. Also, depending on structure of the evolution, we have continuous, discrete, homogeneous, inhomogeneous evolutions, etc. Markov random evolutions in Euclidean spaces are usually called in the literature hidden Markov or regime-switching models. Random evolutions began to be studied in the 1970's, because of their potential applications in finance, insurance, biology, storage, queuing and risk theories, to name a few. In this proposal we introduce a new class of random evolutions, namely, inhomogeneous (or time-inhomogeneous, which does not possess stationary increments) semi-Markov random evolutions and consider their applications in finance, energy and environmental finance. ***The novelty of the proposal is threefold: i) study of a new inhomogeneous semi-Markov process (where transition time distribution between different states of environment is arbitrary, not specific as in Markov case), which switches regimes of evolution; ii) study of a new inhomogeneous random evolutions, constructed by a family of inhomogeneous semi-group of operators, which describe the evolution of our system; iii) applications in finance, energy and environmental finance. To our best knowledge, only homogeneous random evolutions (based on homogeneous Markov or semi-Markov processes, and on homogeneous semi-group of operators) and their applications have been studied.***With financial industry becoming fully computerized, the amount of recorded data, such as high-frequency time-depended data, has exploded. It is seemed then natural to study these data in an inhomogeneous or time-dependent semi-Markov setting. Also, such application as weather derivatives can be useful to hedge the energy derivatives and to construct the hedging portfolios.  The weather derivatives can also be used in environmental case, e.g., together with biotechnology in Canada agriculture sector to reduce vulnerability of crops to environmental changes, and to reduce the risk associated with climate change impact. This research proposal will be a comprehensive tool to integrate not only into the general theory of stochastic processes, but also into the field of their applications in quantitative finance, risk management, and energy and environmental finance. Our models and methods will be applied to Canadian finance, energy and environmental markets, and thus increase our knowledge and awareness of Canadian environmental and sustainability issues.

随机演化，在物理语言中，是随机环境中动态系统的模型，其状态方程受到随机变化的影响;例如，股票/资产在不同的波动率之间切换。在数学语言中，随机演化是由一些随机过程驱动的算子半群（描述系统的演化）的产物。随机过程定义了随机演化的名称：马尔可夫，半马尔可夫，等等。此外，根据演化的结构，我们有连续的，离散的，齐次的，非齐次的演化，等等。随机演化在20世纪70年代开始被研究，因为它们在金融，保险，生物学，存储，排队和风险理论等方面的潜在应用。在这个建议中，我们引入了一类新的随机演化，即非齐次（或时间非齐次，不具有平稳增量）半马尔可夫随机演化，并考虑其在金融，能源和环境金融的应用。* 该提案的新奇有三个方面：i）研究一个新的非齐次半马尔可夫过程（其中不同环境状态之间的转移时间分布是任意的，而不像马尔可夫情形那样是特定的），它转换了演化的机制：ii）研究了由一族非齐次算子半群构造的一个新的非齐次随机演化，它描述了我们系统的演化;（三）金融、能源和环境融资方面的应用。据我们所知，只有齐次随机演化（基于齐次马尔可夫或半马尔可夫过程，以及算子的齐次半群）及其应用被研究过。随着金融业的全面计算机化，记录的数据量，如高频时间依赖数据，已经爆炸。然后，在非齐次或时间依赖的半马尔可夫环境中研究这些数据似乎是很自然的。此外，天气衍生品等应用可以用于对冲能源衍生品和构建对冲组合。天气衍生品还可以用于环境案例，例如，加拿大农业部门的生物技术，以减少作物对环境变化的脆弱性，并减少与气候变化影响有关的风险。这项研究计划将是一个全面的工具，不仅融入随机过程的一般理论，而且还融入其在定量金融，风险管理，能源和环境金融领域的应用。我们的模型和方法将应用于加拿大的金融，能源和环境市场，从而增加我们的知识和加拿大的环境和可持续发展问题的认识。