  The network-based study of financial systems has received considerable
attention in recent years but has seldom explicitly incorporated the dynamic
aspects of such systems. We consider this problem setting from the temporal
point of view and introduce the Interval Debt Model (IDM) and some scheduling
problems based on it, namely: Bankruptcy Minimization/Maximization, in which
the aim is to produce a payment schedule with at most/at least a given number
of bankruptcies; Perfect Scheduling, the special case of the minimization
variant where the aim is to produce a schedule with no bankruptcies (that is, a
perfect schedule); and Bailout Minimization, in which a financial authority
must allocate a smallest possible bailout package to enable a perfect schedule.
We show that each of these problems is NP-complete, in many cases even on very
restricted input instances. On the positive side, we provide for Perfect
Scheduling a polynomial-time algorithm on (rooted) out-trees although in
contrast we prove NP-completeness on directed acyclic graphs, as well as on
instances with a constant number of nodes (and hence also constant treewidth).
When we allow non-integer payments, we show by a linear programming argument
that the problem Bailout Minimization can be solved in polynomial time.
