We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit; more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex cone. Because of these requirements, there are less incentives to operate under a group structure, as creating one single business unit, or altering the liability repartition among units, may allow to reduce the required capital. We analyse the possibilities for the group to benefit from a diversification effect and economise on the cost of capital. We define and study the risk measures that allow for any group to achieve the minimal capital, as if it were a single unit, without altering the liability of business units, and despite the individual admissibility constraints. We call these risk measures cohesive risk measures. In the commonotonic case, we show that they are tail expectations but calculated under a different probability.

我们考虑一个由N组成的群业务部门。我们假设每个单位都有监管限制；更准确地说，要求每个业务单位的净资产属于一组可接受的风险，假设是一个凸锥。由于这些要求，在集团结构下经营的动机较少，因为创建一个单一的业务单位，或改变单位之间的责任重新分配，可能会减少所需的资本。我们分析了集团从多元化效应中受益并节省资本成本的可能性。我们定义和研究允许任何集团实现最低资本的风险措施，就好像它是一个单一的单位，而不改变业务单位的责任，并且尽管有个别的可接纳性限制。我们将这些风险度量称为内聚风险度量。在同调的情况下，