Exotic surplus-dependent risk models and their applications

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Quantitative risk management is a central topic in the fields of insurance and finance, where researchers and practitioners seek the advanced analytic tools and computational methods for better identification, characterization, assessment, management and mitigation of the emerging risks. In the insurance industry, it is of utmost importance to develop such quantitative risk management systems for the solvency risk pertaining to the insurer's ability to meet its future financial obligations. My proposed research program is expected to make significant contributions in this research field through the development and application of analytical approaches and computational methodologies in the study of surplus processes with perturbations in its trajectory. More specifically, my research team and I will concentrate on the following three themes: (1) Stochastic modeling and optimal design with surplus-dependent features; (2) Develop and analyze (surplus-dependent) risk measures for insurance risk processes; (3) Discover potential applications in variable annuities. In Theme (1), following the recent trend in the analysis of an insurer's dynamic cash flows, risk models with surplus-dependent features will be designed and examined to meet the various needs of different parties in insurance practice. Theme (2) studies the surplus-dependent risk measures with a special focus on the drawdown related measures, in order to help provide deeper insight into the characteristics of potential hazards and assist in the early detection of extreme risks. We will also build the connections between ruin theory and risk measures via probabilistic analysis. The integrated outcomes from Themes (1) and (2) will improve the quantitative risk management of solvency risk through the innovative design of dynamic strategies and measurement of the exposures over time. Another contribution of my proposed research program is to expand on the application of exotic risk theory and surplus-dependent risk measures to the pricing and risk management of variable annuity, which is the focus of Theme (3). This research will provide innovative insights for researchers and practitioners in the insurance and finance industries, and train HQP who will be prepared to lead in the related research areas.