Mathematical Challenges in Financial Risk Analysis

本课题的研究内容包括各种风险的概念、计量、分析以及突发情况下的财务风险管理。数学建模，分析，计算（模拟）的方法来解决应用中提出的令人兴奋和具有挑战性的研究问题。 在当前这一代数据丰富的环境下，金融市场中的高频交易算法和高级学习技术成为重要问题。作为一个相对较新的现象，许多讨论都没有坚实的学术研究支持。它们在平时运作并改善市场质量，但在极端情况下可能停止运作，从而导致价格消失（或明显不合理的交易价格）。市场稳定还涉及金融市场的流动性风险问题。在压力时刻，高频交易停止提供流动性，成为流动性的需求者，流动性的提供严重恶化，这会引起大幅波动。市场参与者会对即时信息做出反应，换句话说，噪音会产生噪音。 无论是模型还是使用它们的人，都缺乏明确表达基础风险和与实际市场相关的风险的能力。模型变得更加复杂，但同样的逻辑仍然存在。今天，通过重新确定风险暴露，开发新的风险分析工具（并培训专业人员）至关重要。探索新的研究方法以应对当前的挑战比以往任何时候都更加重要，而这一提议反映了这一新趋势的很大一部分。

My research project consists of the conception of various risks, the measurement, the analysis, and the management of financial risks under unexpected circumstances. Mathematical modeling, analyzing, computing (simulations) approaches are required to solve the exciting and challenging research problems proposed in the application. In the current generation of data-rich environment, high-frequency trading algorithms and advanced learning techniques in financial markets become important issues. As a relatively new phenomenon, much of the discussion is not backed by solid academic research. They operate and improve market quality in usual times, but may stop operating and thus cause the prices to disappear (or clearly unreasonable traded prices) in extreme circumstances. Market stability also relates to the issue of liquidity risk in financial markets. At the time of stress, the high-frequency trading stops providing liquidity and becomes the demander of liquidity, the provision of liquidity seriously deteriorates, which can cause substantial volatility. This is explained by the fact that market participants react to immediate information, in other words, that noise creates noise. Both the models and the people who use them are lacking the ability to articulate the risk of the underlying and that related to the actual market. Models become more sophisticated, but the same logic has persisted. Today, it is crucial to develop new tools (and train professionals) for risk analysis, by reworking on the determination of the exposure to risk. It is more important than ever to explore new research approaches for facing current challenges, and this proposal reflects a big part of this new trend.