The bankruptcy problem is to divide a homogeneous divisible good (the “estate”) between claimants, when the sum of the claims exceeds the value of the estate. When the problem is looked at from an ex-ante point of view (i.e. before the size of the estate is revealed), it is possible to formulate a notion of Pareto efficiency that is stronger than when the more common ex-post perspective is taken. Under the assumption of common beliefs, the strong notion of efficiency leads, in combination with the requirement that all claims should be fulfilled when the value of the estate is equal to the sum of the claims, to a uniquely defined division rule when utility functions for all agents are given. The resulting rule can be represented in the form of a parametric function. For the case in which all agents are equipped with the same utility function, the class of parametric functions that can be obtained in this way is characterized. In particular, it is shown that two well-known division rules for the bankruptcy problem, namely Constrained Equal Losses and Proportional Division, can be rationalized under strong Pareto efficiency by constant absolute risk aversion and constant relative risk aversion respectively.

破产问题是当索赔总额超过遗产价值时，将均等的可分割商品（“房地产”）分配给索赔人。当从事前的角度看问题时（即在揭露遗产的规模之前），有可能提出帕累托效率的概念，该概念比采取更普遍的事后观点更强。在共同信念的假设下，效率的强力概念与以下要求相结合：当遗产的价值等于要求之和时，必须满足所有要求，当效用为给出了所有代理。所得规则可以参数函数的形式表示。如果所有座席都具有相同的效用功能，可以以此方式获得的参数函数的类别进行了表征。特别是，证明了在破产问题上的两个著名的划分规则，即约束相等损失和比例划分，可以在帕累托效率较高的情况下分别通过恒定的绝对风险规避和恒定的相对风险规避来合理化。