Inf-convolution of convex risk emasures and optimal risk transfer

We develop a methodology to optimally design a financial issue to hedge

non-tradable risk on financial markets.The modeling involves a minimization

of the risk borne by issuer given the constraint imposed by a buyer who

enters the transaction if and only if her risk level remains below a given

threshold. Both agents have also the opportunity to invest all their residual

wealth on financial markets but they do not have the same access to financial

investments. The problem may be reduced to a unique inf-convolution problem

involving some transformation of the initial risk measures.