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.

在主业务线及其子业务线之间分配给定的总资本时，决策者将面临每个业务线的资本短缺风险和资本过剩风险。这两种风险之间存在权衡。为了平衡主业务线及其子业务线的这两种风险，我们提出了一种在分层公司结构中同时考虑资本短缺风险和资本过剩风险的资本配置模型。我们推导出最优分配原则作为最小化平衡短缺和过剩风险的一般损失函数的解决方案。作为所提出模型的应用，推导出了存在分层公司结构的一般比例分配原则。说明了一般比例分配可以看作是在所提出的模型中最小化指定损失函数的唯一解决方案。讨论了该模型与一些风险因素（如依赖性、极端事件、外生风险和风险措施）之间的联系。