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: 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=635731
• 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.

在物理语言中，随机进化是一个动态系统在随机环境中的模型，它的状态方程是随机变化的；例如，在不同波动率之间转换的股票/资产。在数学语言中，随机进化是由一些随机过程驱动的半群算子（描述系统的进化）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。同样，根据进化的结构，我们有连续的、离散的、均匀的、非均匀的进化等等。欧几里得空间中的马尔可夫随机演化在文献中通常称为隐马尔可夫模型或状态切换模型。随机进化在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有潜在的应用。在这个提议中，我们引入了一类新的随机进化，即非齐次（或时间非齐次，不具有平稳增量）半马尔可夫随机进化，并考虑了它们在金融、能源和环境金融中的应用。