Optimal capital allocation principles considering capital shortfall and surplus risks in a hierarchical corporate structure

摘要

When allocating a given total capital among main business lines and their sub-business lines, a decision maker will face both capital shortfall risk and capital surplus risk for each business line. There is a trade-off between the two kinds of risks. To balance such two kinds of risks in main business lines and their sub-business lines, we propose a capital allocation model considering both capital shortfall risks and capital surplus risks in a hierarchical corporate structure. We derive optimal allocation principles as solutions that minimize a general loss function that balances the shortfall and surplus risks. As applications of the proposed model, a general proportional allocation principle in the presence of a hierarchical corporate structure is derived. It is illustrated that the general proportional allocation can be viewed as the unique solution minimizing a specified loss function in the proposed model. Connections between this proposed model and some risk factors, such as dependence, extreme events, exogenous risks, and risk measures, are discussed. (C) 2021 Elsevier B.V. All rights reserved.