We discuss risk evaluation and risk-averse optimization of complex distributed systems with general risk functionals.

A set of axioms for the functionals evaluating the total risk of the system is postulated, which allows us to establish the dual representation for the systemic risk measures. We propose two families of measures constructed by using either collections of linear scalarizations or non-linear risk aggregators. We address the challenges associated with high-dimensional risk, the need to evaluate

the risk of every agent using confidential or proprietary information, and the requirement of fair risk allocation to the agents.

Two stochastic programming problem with the new measures of high-dimensional risks are formulated and illustrated by two applications: operation of a team of robots exploring an area and a disaster management problem. Our experiments demonstrate that the proposed approach facilitates fair risk allocation.

This is a joint work with Aray Almen, JPMorgan Chase.