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.

大数据已成为许多领域，保险和能源市场的建筑分析，以便在这些领域中出现的大数据，我们侵犯了不同的一般化合物霍克斯流程（GCHP）过程（MRP）以更长的时间尺度，秒或分钟的范围，而不是毫秒，然后渐近的方法与内盘价格和阶数流量之间的链接，以较长的时间尺度，几分钟或几分钟的形式建模我们的动力学。叔叔限制定理（FCLT），我们使用实际数据来证明我们的结果和比较分析。也研究了MRP和GCHP模型的最佳清算，尤其是在风险理论中，考虑了一个核心问题。索赔到达的模型在GCHP上。时间的时间破坏概率。为了避免全球经济的最糟糕的后果，必须通过引入碳CE温室气体发出的碳化力来脱碳。征收电力从煤炭转换为天然气，最终从天然气，太阳能或其他可再生能源转换能源市场中的现货价格很长。可以使用我们的随机模型，分析和方法来完成。