  Financial networks are characterized by complex structures of mutual
obligations. These obligations are fulfilled entirely or in part (when defaults
occur) via a mechanism called clearing, which determines a set of payments that
settle the claims by respecting rules such as limited liability, absolute
priority, and proportionality (pro-rated payments). In the presence of shocks
on the financial system, however, the clearing mechanism may lead to cascaded
defaults and eventually to financial disaster. In this paper, we first study
the clearing model under pro-rated payments of Eisenberg and Noe, and we derive
novel necessary and sufficient conditions for the uniqueness of the clearing
payments, valid for an arbitrary topology of the financial network. Then, we
argue that the proportionality rule is one of the factors responsible for
cascaded defaults, and that the overall system loss can be reduced if this rule
is lifted. The proposed approach thus shifts the focus from the individual
interest to the overall system's interest to control and contain adverse
effects of cascaded failures, and we show that clearing payments in this
setting can be computed by solving suitable convex optimization problems.
