15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Minisymposium Finanzmathematik
Donnerstag, 20. September 2001, 14.00, Audimax der Universität Wien


Super-replication in finance and geometric flows

Mete Soner, Koc University, Istanbul


In perfect financial markets derivative securities can be perfectly replicated by replicated by appropriately investing in the underlying market. Altough in most markets perfect replication is not possible, it is still possible to super-replicate. Mathematically replication means to have zero wealth with probability one at the end, while super-replication requires to have nonnegative wealth. Of course in addition to the properties of the underlying financial market, the initial position that we have also determines whether we could replicate or super-replicate. In this talk I will show techniques to characterize the set of initial data that would allow super-replication and the evolution of these sets over time. This evolution problem is necessarily a geometric one and with appropriate model choices classic flows such as mean curvature flow can also be obtained.

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