Hedging under multiple risk constraints

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 at a sequence of future dates. For a specified loss function, the shortfall with respect to each of the benchmarks weighted by this loss function must remain bounded in expectation by a given threshold. We consider different risk constraints and alternative formulations of this problem in a complete market setting, and establish the relationship between these formulations. By using a recursive dynamic programming method, we solve the hedging problems in a general non-Markovian context and give explicit solutions in special cases. We finally present applications to an actual asset-liability management problem of an energy company in a realistic setting.