  Motivated by the asset-liability management of a nuclear power plant
operator, we consider the problem of finding the least expensive portfolio,
which outperforms a given set of stochastic benchmarks. For a specified loss
function, the expected shortfall with respect to each of the benchmarks
weighted by this loss function must remain bounded by a given threshold. We
consider different alternative formulations of this problem in a complete
market setting, establish the relationship between these formulations, present
a general resolution methodology via dynamic programming in a non-Markovian
context and give explicit solutions in special cases.
