  Systemic risk is concerned with the instability of a financial system whose
members are interdependent in the sense that the failure of a few institutions
may trigger a chain of defaults throughout the system. Recently, several
systemic risk measures have been proposed in the literature that are used to
determine capital requirements for the members subject to joint risk
considerations. We address the problem of computing systemic risk measures for
systems with sophisticated clearing mechanisms. In particular, we consider an
extension of the Rogers-Veraart network model where the operating cash flows
are unrestricted in sign. We propose a mixed-integer programming problem that
can be used to compute clearing vectors in this model. Due to the binary
variables in this problem, the corresponding (set-valued) systemic risk measure
fails to have convex values in general. We associate nonconvex vector
optimization problems with the systemic risk measure and provide theoretical
results related to the weighted-sum and Pascoletti-Serafini scalarizations of
this problem. Finally, we test the proposed formulations on computational
examples and perform sensitivity analyses with respect to some model-specific
and structural parameters.
