A one-step approach for determining the optimal aggregate capital reserve and allocation

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 discussed in. Additionally, we provide numerical examples to illustrate our new approaches and compare them with standard methods commonly used in practice.