Model uncertainty and robustness in risk management

该提案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鲁棒性的统计和计算方法。模型的不确定性和稳健性问题，涉及“不正确、不合理或滥用的模型产出和报告”，已成为当前风险管理和监管挑战的核心组成部分。我们解决模型的不确定性沿着几个方向的实际重要性，在金融和保险。首先，由于高维统计建模和数据限制的挑战，风险聚集中的依赖不确定性在实践中是一个具有挑战性但又常见的情况，近年来已经成为风险管理中非常热门的研究课题。众所周知，开发一个风险评估程序，允许计算实际上可采用的评估依赖不确定性下的风险聚集是极具挑战性的。我们解决这个问题，借用技术，从最近的研究进展，在文献中的强大的优化和依赖建模。其次，我们研究风险度量和风险优化中的鲁棒性问题，从而解决根据稍微错误的假设（最相关的情况）管理和优化风险的定量后果。第三，我们将模型不确定性引入到风险分担和经济均衡问题中，并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。沿着这条路，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，copula，博弈论，统计鲁棒性，非凸优化和概率组合学。通过对风险和不确定性的全面理解，拟议的研究将为定量风险管理领域做出重大贡献。预期的结果将提供新的理论见解，并将导致在各个实际领域的进步，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的发展有广泛的应用，在一个复杂的模型中的不确定性，从而在其他领域，如运筹学，管理科学，自然科学，信息学和统计学是有用的。数据分析也将发挥重要作用，我们将主要处理财务数据。HQP将积极参与研究过程。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.