Reinsurance of multiple risks with generic dependence structures

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