Monday, December 4, 2000


Ioannis Karatzas
Departments of Mathematics and Statistics
Columbia University

CONVEX DUALITY IN HYPOTHESIS TESTING AND IN PARTIAL HEDGING

We discuss two, apparently rather different, problems the Testing of Composite Hypotheses versus Composite Alternatives (a classical question in Mathematical Statistics), and the Partial Hedging of Contingent Claims (a relatively new issue in the "young" field of Mathematical Finance).

We show that the same tools, drawn from non-smooth convex analysis and duality theory, can be used to treat each of these problems -- and that they provide almost identical solutions.