Inf-convolution of risk measures 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.