Quantitative Risk Management under Model Uncertainty: Reinsurance, Capital Allocation, and Systemic Risk

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Insurance companies and financial institutions are facing increasing and more complex risks because of the rising number of extreme events, such as the global financial crisis of 2007-08, the global COVID-19 pandemic, and wild forest fires. New risk models and risk management methods are pressingly needed for modern quantitative risk management (QRM) in insurance and finance. A crucial aspect in QRM is how to measure, model and manage risks to be faced by insurance companies and financial institutions.  Existing tools and techniques of QRM are based largely on the assumption that the complete distributional information of risks is known. However, in most practical situations, only the partial distributional information of risks is available. Sometimes only means and variances of risks are available, while other times only the marginal distributions of risks are known but the dependence structure of risks is unknown, or the distribution parameters of risks are uncertain. All such situations or uncertainties are referred to as model uncertainty, which is an important issue in QRM.  In this proposed research, I will focus on how to model and manage risks of insurance and finance under model uncertainty.   The long-term objective of my research program is to provide novel models and practical solutions for QRM in insurance and finance under model uncertainty and enable decision-makers of QRM to have a better understanding of the risks resulting from model uncertainty. The short-term objectives of my research program are as follows: (A) Develop innovative models and methods for optimal reinsurance under distributional uncertainty; (B) Provide optimal reinsurance solutions for insurance portfolios under dependence uncertainty; (C) Develop one-step schemes for determining capital requirements for risk portfolios; and (D) Manage systemic risks of insurance and finance portfolios by optimal capital allocation schemes. The innovation of the proposed research lies in addressing the critical issue of model uncertainty in QRM for insurance and finance, providing novel optimal reinsurance models and practical solutions for insurance companies to deal with model uncertainty, and managing systemic risks in insurance and finance by optimal capital allocation schemes. The one-step schemes for determining capital requirements developed in this research will help the regulators to stipulate more reasonable capital requirements for insurance companies and financial institutions. The questions addressed in this research program are important and timely. Students involved in this research program will learn how to propose and model QRM problems from a practical perspective, how to solve problems by developing new skills and employing the cutting-edge technologies. Through the training in this program,  students will gain knowledge and skills of QRM to enable them to successfully find jobs in academia or insurance and finance industries.