Abstract
This paper addresses the stochastic differential utility (SDU) version of the issue raised by Barrieu and El Karoui (Quantitative Finance, 2:181–188, 2002a) in which optimal risk transfer from a bank to an investor, realized by transacting well-designed derivatives written on relevant illiquid assets, was␣mainly studied in two cases with and without an available financial market. From a stochastic maximum principle as described in Yong and Zhou (Stochastic controls: Hamiltonian systems and HJB equations. Springer-Verlag, New York, 1999) we shall derive necessary and sufficient conditions for optimality in several SDU-based maximization problems. It is also shown that the optimal risk transfer, consumptions, investment policies of both agents are characterized by a forward–backward stochastic differential equation (FBSDE) system.
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