15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung
16. bis 22. September 2001 in Wien
Minisymposium Finanzmathematik
Donnerstag, 20. September 2001, 15.00, Audimax der Universität Wien
On the problem of optimal investment with random endowment in incomplete markets
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.
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