Grant: Discovery Grants Program - Individual

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.