Ex-Ante Estate Division under Strong Pareto Efficiency

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. A characterization is given of the parametric functions that can be obtained in this way when all agents are equipped with the same utility function. 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