Parametric Rules for State Contingent Claims

We study bankruptcy rules in a setting where individuals have state contingent claims. A rule must distribute shares before uncertainty resolves. Within a wide class of parametric rules, we first characterize rules of ex-ante form in terms of the way that the rule processes inherent uncertainty in the individual claims. The key property is: No Penalty for Risk. It says that the rule does not penalize an individual in a situation that differs from another only in terms of the this individual's claim in that the former situation has a risky version of the riskless claim in the latter situation. With regard to the ex-post characterization, our key property is: Indifference to Independent Combinations. It says that if an individual is risk neutral with expected utility preferences then any rule that makes her indifferent between any bankruptcy problem and a corresponding independent combination of gamble between a degenerate gamble and a zero game (any bankruptcy game with zero endowment) forces the rule to be in the ex-post form. Finally, a partial comparative static result is provided which formalizes the claim that individuals generally and ex-ante rules more appealing when the level of the resource is suffciently low.