报告题目：A one-step approach for determining the optimal aggregate capital reserve and allocation

报 告 人：蔡军（加拿大滑铁卢大学教授）

报告时间：2024年11月15日下午 15:30-

报告地点： 格物楼数统院402智慧教室

报告摘要：Capital requirements for financial or insurance companies are crucial regulatory standards. Various approaches exist for determining and allocating aggregate capital reserve. A commonly used method is a two-step approach: first, it determines the total required reserve for a company based on a capital requirement criterion, and then it allocates this total reserve to its business units using a capital allocation principle. While the aggregate capital determined by the capital criterion may be optimal for aggregate losses, the allocation principle may only be optimal for individual losses. Combining these two steps can lead to capital requirements that are not optimal and may even be unreasonable. In this paper, we introduce a new method for determining the optimal aggregate capital reserve and the corresponding optimal allocation through a one-step approach, allowing for the simultaneous consideration of aggregate and individual risks. In our one-step approach, both the aggregate capital and the allocation scheme are optimized to minimize an expected loss or cost function that accounts for these risks. Our findings provide insights into decision-makers' attitudes toward commonly used capital requirement criteria and allocation principles, including VaR and CTE capital criteria, as well as VaR-based and CTE-based haircut allocation principles, and the CTE additive allocation principle. We also offer quantitative arguments explaining why the aggregate capital requirement and the corresponding allocation are optimal and specify the conditions under which they achieve optimality. Notably, our one-step optimal capital criteria can yield required reserves that meet the safety and budget requirements. Additionally, we provide numerical examples to illustrate our new approaches and compare them with standard methods commonly used in practice.

报告人简介：Dr. Jun Cai is a professor in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada. His research interests encompass actuarial science, applied probability, mathematical finance, and operations research. Currently, he focuses on quantitative risk management for insurance and finance, insurance decision problems, dependence modeling, and risk analysis with model uncertainty. His publications have appeared in leading journals such as Operations Research, European Journal of Operational Research, Mathematical Finance, Finance and Stochastics, Journal of Risk and Insurance, Insurance: Mathematics and Economics, ASTIN Bulletin, Scandinavian Actuarial Journal, Advances in Applied Probability, Journal of Multivariate Analysis, and Stochastic Processes and their Applications. Additionally, he and Dr. Tiantian Mao were awarded the 2020 International Actuarial Association (IAA) Bob Alting von Geusau Prize. He also serves as an associate editor for Insurance: Mathematics and Economics.