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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759139
• 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.

现在，大数据已成为许多领域建立和分析的驱动力，包括财务，保险和能源市场。该提案致力于对这些领域产生的大数据的随机建模和分析。在金融中，我们引入了不同的一般复合鹰队过程（GCHP）和Markov续订过程（MRP），以建模限制订单簿（LOB）的动力学。为了处理大数据，我们考虑了更长的时间尺度，几秒钟或几分钟的动态，而不是毫秒，然后应用渐近方法来研究室内价格挥发率与LOB中的订单流之间的联系，即大数量（LLN）定律（LLN）和功能中心极限定理（FCLT）。我们使用实际数据来证明和实施我们的结果。进行定量和比较分析以找出描述LOB实际动力学的最佳模型。还研究了描述许多股票中价动力学的多元一般化合物霍克斯工艺。 MRP和GCHP模型都考虑最佳清算，获取和市场制作问题。在保险中，尤其是在风险理论中，一个核心问题是如何建模描述大量索赔事件的随机过程。我们研究具有基于GCHP的索赔到达的风险模型。我们表明，它适合对经验保险数据进行建模。使用该模型的LLN和FCLT等渐近方法，我们首先得出净利润条件，然后分别提出纯扩散近似，从而可以分析有限的时间和无限时间的破坏可能性。应用此近似值，我们还将研究不完整市场中保险公司的最佳投资策略。在能源市场中，我们还存在处理大数据的问题，例如，现货价格大量变化。为了避免攀岩变化的最糟糕后果，必须通过引入碳税来减少温室气体排放来大大脱碳，例如，全球经济的能源链必须大大脱碳。我们根据来自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促使电力生产商从煤炭转变为天然气的必要税，这是碳密集型较少的，然后最终从天然气转换为风，太阳能，水力，或其他可再生能源。我们将考虑几种类型的随机模型，包括基于征费的OU模型，并提供比较分析哪种模型是最好的。我们使用GCHP来建模群集效应和能源市场现货价格的长期内存特性。绝对有可能将化石燃料能量从化石燃料能源带到清洁和可再生能源中：美国一组工程已经计算出，如果我们决定这样做，加拿大可能会完全由可再生能源提供动力。特别是在此提案中，我们将展示如何使用我们的随机模型，分析和方法来完成它。