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.