Stochastic bankruptcy games

We study bankruptcy problems where the estate and the claims have stochastic values and we allow these values to be correlated. We associate a transferable utility game with uncertainty to a stochastic bankruptcy problem and use the Weak Sequential Core as a solution concept for such games. We test the stability of a number of well known division rules in this stochastic setting and find that all of them are unstable, with the exception of the stochastic extension of the Constrained Equal Awards rule which leads to a Weak Sequential Core element.