(Joint work with Uwe Schmock and Uwe Wystup. The paper is available at http://www.math.cmu.edu/users/shreve)

Abstract:

Options with discontinuous payoffs are generally
traded above their theoretical Black-Scholes prices because
of the hedging difficulties created by their large delta
and gamma values. A theoretical method for pricing these
options is to constrain the hedging portfolio and
incorporate this constraint into the pricing by computing
the smallest initial capital which permits
super-replication of the option. We develop this idea for
exotic options, in which case the pricing problem becomes
one of stochastic control. Our motivating example is a call
which knocks out in the money, and explicit formulas for
this and other instruments are provided.