  We consider the optimal reinsurance problem from the point of view of a
direct insurer owning several dependent risks, assuming a maximal expected
utility criterion and independent negotiation of reinsurance for each risk.
Without any particular hypothesis on the dependency structure, we show that
optimal treaties exist in a class of independent randomized contracts. We
derive optimality conditions and show that under mild assumptions the optimal
contracts are of classical (non-randomized) type. A specific for mof the
optimality conditions applies in that case. We present a numerical scheme to
solve the optimality conditions.
