Model uncertainty and robustness in risk management

这项建议的总体目标是发展数学和经济理论，以及金融和保险风险管理中模型不确定性和稳健性的统计和计算方法。与“不正确、不合理或滥用的模型产出和报告”有关的模型不确定性和稳健性问题，似乎已成为当前风险管理和监管挑战的核心组成部分。我们沿着金融和保险中几个具有实际重要性的方向解决了模型的不确定性。首先，由于高维统计建模和数据限制的挑战，风险聚集中的相关性不确定性是一种具有挑战性的实际情况，近年来成为风险管理中的一个非常热门的研究课题。众所周知，制定一种风险评估程序，以便在相关性不确定的情况下计算可实际使用的风险聚合评估，是非常具有挑战性的。我们通过借用稳健优化和依赖建模文献中最近的研究进展来解决这个问题。其次，我们研究了风险度量和风险优化中的稳健性问题，从而解决了根据略微错误的假设管理和优化风险的量化后果，这是一个最相关的情况。第三，将模型不确定性引入风险分担和经济均衡问题，分析了模型不确定性和异质信念在复杂金融系统中的作用。在这一过程中，我们为与上述问题相关的领域开发了深刻的数学工具，如测度论、决策论、Copulas、博弈论、统计稳健性、非凸优化和概率组合学。*通过全面理解风险和不确定性，所提出的研究将对定量风险管理领域做出重大贡献。预期结果将提供新的理论见解，并将在各个实践领域取得进展，包括监管政策制定、企业风险管理和经济决策。所提出的数学和统计发展在复杂模型中的不确定性方面具有广泛的应用，因此在运筹学、管理科学、自然科学、信息学和统计学等其他领域也很有用。数据分析也将发挥重要作用，我们将主要处理金融数据。HQP将深入参与研究过程。他们将获得进行研究和实施数据科学技术的技能，学习统计学、精算学和风险管理方面的知识，并通过拟议的研究满足研究生课程的研究要求。

The overall aim of this proposal is to develop the mathematical and economic theory as well as statistical and computational methods for model uncertainty and robustness in financial and insurance risk management. Model uncertainty and robustness issues, concerning “incorrect, unjustified or misused model outputs and reports", have appeared as a central component of the current challenges in risk management and regulation. We address model uncertainty along several directions of practical importance in finance and insurance. First, dependence uncertainty in risk aggregation, as a challenging yet common situation in practice due to challenges in high-dimensional statistical modeling and data limitation, has recently been a very popular research topic in risk management. Developing a risk evaluation procedure which allows for computing practically employable assessments of risk aggregation under dependence uncertainty is well known to be highly challenging. We address this problem by borrowing techniques from recent research development in the literature of robust optimization and dependence modeling. Second, we investigate robustness issues in risk measures and the optimization of risk, thus addressing the quantitative consequences of managing and optimizing risks according to slightly wrong assumptions, a most relevant situation. Third, we bring model uncertainty into the problems of risk sharing and economic equilibrium for various settings of risk managers and financial contexts, and analyze the effect of model uncertainty and heterogeneous beliefs in a complex financial system. Along the way, we develop profound mathematical tools for fields related to the above problems, such as measure theory, decision theory, copulas, game theory, statistical robustness, non-convex optimizations, and probabilistic combinatorics.******The proposed research will contribute significantly to the field of quantitative risk management via a comprehensive understanding of risk and uncertainty. The anticipated results will provide novel theoretical insights and will lead to advances in various practical domains, including regulatory policy making, enterprise risk management and economical decision making. The proposed mathematical and statistical developments have wide applications wherever uncertainty in a complex model is concerned, thus being useful in other fields such as operations research, management science, natural sciences, informatics, and statistics. Data analysis will also play an important role and we shall mainly work with financial data. HQP will be intensively involved in the research process. They will gain skills in conducting research and implementing data science technologies, learn knowledge in statistics, actuarial science and risk management, and fulfill the research requirements in their graduate programs through the proposed research.