Dmitry Kramkov, Carnegie Mellon University
Recently J. Cvitanic, W. Schachermayer and Wang H. studied the problem
of optimal investment with random endowment using a duality approach. In
contrast with the classical case (no endowment) the solution of the dual problem
defined in their paper exists provided its domain includes general linear
functionals on , i.e. finitely additive measures.
In this paper we formulate and study a new dual problem to the problem of optimal investment with random endowment. This approach permits us to prove the existence of the solution of the dual problem in , which is similar to the classical case. Is is also useful for other applications in finance such as the utility based pricing. The presentation is based on a joint project with Julian Hugonnier.