  The question of pricing and hedging a given contingent claim has a unique
solution in a complete market framework. When some incompleteness is
introduced, the problem becomes however more difficult. Several approaches have
been adopted in the literature to provide a satisfactory answer to this
problem, for a particular choice criterion. In this paper, in order to price
and hedge a non-tradable contingent claim, we first start with a (standard)
utility maximization problem and end up with an equivalent risk measure
minimization. This hedging problem can be seen as a particular case of a more
general situation of risk transfer between different agents, one of them
consisting of the financial market. In order to provide constructive answers to
this general optimal risk transfer problem, both static and dynamic approaches
are considered. When considering a dynamic framework, our main purpose is to
find a trade-off between static and very abstract risk measures as we are more
interested in tractability issues and interpretations of the dynamic risk
measures we obtain rather than the ultimate general results. Therefore, after
introducing a general axiomatic approach to dynamic risk measures, we relate
the dynamic version of convex risk measures to BSDEs.
