Stochastic Modelling of Big Data in Finance, Insurance and Energy Markets

金融、保险和能源市场大数据的随机建模

• 批准号: RGPIN-2020-03948
• 负责人: Swishchuk, Anatoliy
• 金额: $ 1.75万
• 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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=739583
• 关键词: Stochastic; Modelling; Big; Data; Finance

Big data has now become a driver of models building and analysis in a number of areas, including finance, insurance and energy markets. The proposal is devoted to stochastic modelling and analyzing of big data arising in these areas.  In finance, we introduce different general compound Hawkes processes (GCHP) and Markov renewal processes (MRP) to model the dynamics of limit order book (LOB). To deal with big data, we consider our dynamics on a longer time scale, seconds or minutes, instead of milliseconds, and then applying the asymptotic methods to study the link between intraday price volatilities and order flows in LOB, i.e., law of large numbers (LLN) and functional central limit theorems (FCLT). We use real data to justify and implement our results. Quantitative and comparative analyses are performed to find out which model is the best in describing the real dynamics of LOB. Multivariate general compound Hawkes process describing the dynamics of the mid-price of many stocks is studied as well. Optimal liquidation, acquisition and market making problems consider for both MRP and GCHP models. In insurance, in particular in risk theory, a central question is how to model the random process describing a big number of claim occurrences. We study a risk model with claim arrivals based on GCHP. We show that it is suitable to model empirical insurance data. Using asymptotic methods, such as LLN and FCLT for this model, we derive net profit condition first, and then present a pure diffusion approximation, respectively, which allow analytical calculation of finite-time and infinite-time ruin probabilities. Applying this approximation, we will also study an optimal investment strategies for an insurer in an incomplete market. In energy markets, we also have a problem of dealing with big data, e.g., a big number of spot price changes. To avoid the worst consequences of climate change, the energy chain of the global economy must be drastically decarbonized, e.g., by introducing a carbon tax to reduce greenhouse gas emissions. We study the correct approach to carbon pricing based on big data from different energy markets. We define the carbon price as the necessary tax to incite electricity producers to switch from coal to natural gas, which is less carbon intensive, and then ultimately switching from natural gas to wind, solar, hydro, or other clean and renewable energy. We will consider several types of stochastic models, including Levy-based OU models, and give comparative analyses which model is the best. We use GCHP to model clustering effects and long memory properties of spot prices in energy markets. A path out of fossil fuel energy into the clean and renewable energy is definitely possible: a group of US engineering has calculated that Canada could be completely powered by renewable energy if we just decide to do it. In this proposal, in particular, we will show how it can be done using our stochastic models, analyses and methodologies.

大数据现已成为金融、保险和能源市场等多个领域模型构建和分析的驱动力。该提案致力于对这些领域中出现的大数据进行随机建模和分析。  在金融领域，我们引入不同的通用复合霍克斯过程（GCHP）和马尔可夫更新过程（MRP）来模拟限价订单簿（LOB）的动态。为了处理大数据，我们在更长的时间尺度（秒或分钟，而不是毫秒）上考虑我们的动态，然后应用渐近方法来研究日内价格波动和 LOB 中的订单流之间的联系，即大数定律（LLN）和函数中心极限定理（FCLT）。我们使用真实数据来证明和实施我们的结果。进行定量和比较分析，以确定哪种模型最能描述 LOB 的真实动态。还研究了描述许多股票中间价格动态的多元一般复合霍克斯过程。 MRP 和 GCHP 模型均考虑最佳清算、收购和做市问题。 在保险领域，特别是在风险理论中，一个中心问题是如何对描述大量索赔事件的随机过程进行建模。我们研究了基于 GCHP 的索赔到达风险模型。我们证明它适合对经验保险数据进行建模。对于该模型，我们使用渐近方法（例如 LLN 和 FCLT），首先推导净利润条件，然后分别提出纯扩散近似，从而允许分析计算有限时间和无限时间破产概率。应用这种近似，我们还将研究保险公司在不完全市场中的最佳投资策略。 在能源市场中，我们还面临着处理大数据的问题，例如大量的现货价格变化。为了避免气候变化最严重的后果，全球经济的能源链必须大幅脱碳，例如通过征收碳税来减少温室气体排放。我们根据不同能源市场的大数据研究正确的碳定价方法。我们将碳价格定义为必要的税收，以激励电力生产商从煤炭转向碳密集度较低的天然气，然后最终从天然气转向风能、太阳能、水力或其他清洁和可再生能源。我们将考虑几种类型的随机模型，包括基于 Levy 的 OU 模型，并比较分析哪种模型是最好的。我们使用 GCHP 来模拟能源市场现货价格的集群效应和长记忆特性。从化石燃料能源转向清洁和可再生能源的道路绝对是可能的：一组美国工程人员计算出，如果我们决定这样做，加拿大可以完全由可再生能源提供动力。 特别是在本提案中，我们将展示如何使用我们的随机模型、分析和方法来实现这一目标。