Bancruptcy in a model of unsecured claims

We study a two periods model of incomplete markets with nominal assets unsecured by collateral, where agents can go bankrupt but there are no bankruptcy penalties entering directly in the utility function. We address two cases: first, a proportional reimbursement rule under bounded short sales and limited liability and, secondly, a nonproportional reimbursement rule, favoring smaller claims, without bounds on short-sales, but assuming that liability approaches total garnishment as debt goes to infinity.