  A fundamental problem in risk management is the robust aggregation of
different sources of risk in a situation where little or no data are available
to infer information about their dependencies. A popular approach to solving
this problem is to formulate an optimization problem under which one maximizes
a risk measure over all multivariate distributions that are consistent with the
available data. In several special cases of such models, there exist dual
problems that are easier to solve or approximate, yielding robust bounds on the
aggregated risk. In this chapter we formulate a general optimization problem,
which can be seen as a doubly infinite linear programming problem, and we show
that the associated dual generalizes several well known special cases and
extends to new risk management models we propose.
