  In this paper, we deal with risk evaluation and risk-averse optimization of
complex distributed systems with general risk functionals. We postulate a novel
set of axioms for the functionals evaluating the total risk of the system. We
derive a dual representation for the systemic risk measures and propose a way
to construct non-trivial families of measures by using either a collection of
linear scalarizations or non-linear risk aggregation. The new framework
facilitates risk-averse sequential decision-making by distributed methods. The
proposed approach is compared theoretically and numerically to some of the
systemic risk measurements in the existing literature.
  We formulate a two-stage decision problem with monotropic structure and
systemic measure of risk. The structure is typical for distributed systems
arising in energy networks, robotics, and other practical situations. A
distributed decomposition method for solving the two-stage problem is proposed
and it is applied to a problem arising in communication networks. We have used
this problem to compare the methods of systemic risk evaluation. We show that
the proposed risk aggregation leads to less conservative risk evaluation and
results in a substantially better solution of the problem at hand as compared
to an aggregation of the risk of individual agents and other methods.
