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.

在物理语言中，随机进化是在随机环境中的动态系统的模型，其状态方程会受到随机变化的影响；例如，一种在不同挥发性之间切换的库存/资产。在数学语言中，随机进化是由某些随机过程驱动的半集合（描述系统演变）的产物。随机过程定义了随机演变的名称：马尔可夫，半马尔可夫等。另外，取决于进化的结构，我们具有连续，离散，均匀的，均匀的，不均匀的演变等。马尔可夫在欧几里得空间中的随机进化通常在文学隐藏的Markov或Sident Markov或Sendicime-Switching模型中被称为。随机演变在1970年代开始研究，因为它们在金融，保险，生物学，存储，排队和风险理论中的潜在应用，仅举几例。在此提案中，我们介绍了一种新的随机发展类别，即不均匀（或不具有固定增量的时间均匀增量）半马尔可夫随机演变，并考虑其在金融，能源和环境融资中的应用。 ***该提案的新颖性是三重的：i）研究一种新的不均匀半马尔科夫过程（其中不同环境之间的过渡时间分布是任意的，而不是马尔可夫案中的特定特定），这会切换进化的状态； ii）研究一种新的不均匀随机演变，该进化是由一个不均匀的半集团的家族构建的，描述了我们系统的演变； iii）在金融，能源和环境融资中申请。据我们所知，只有同质的随机发展（基于马尔可夫或半马尔可夫流程，以及均质的半集团运营商）及其应用。当时似乎很自然地在不均匀或时间依赖的半马尔可夫环境中研究这些数据。同样，天气衍生物之类的应用对于对冲能源衍生品和构建对冲投资组合可能很有用。天气衍生物也可以用于环境案例，例如，加拿大农业领域的生物技术，以减少农作物对环境变化的脆弱性，并降低与气候变化影响相关的风险。该研究建议将成为一种综合工具，不仅将其集成到随机过程的一般理论中，还将成为其在定量融资，风险管理以及能源和环境金融领域的应用领域。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，从而提高我们对加拿大环境和可持续性问题的知识和认识。