Static Hedging of Barrier Options with a Smile: An Inverse Problem
Let L be a parabolic second order differential operator on the domain Given a function and such that the support of û is contained in , we let be the solution to the equation: Given positive bounds we seek a function u with support in such that the corresponding solution y satisfies: We prove in this article that, under some regularity conditions on the coefficients of L, continuous solutions are unique and dense in the sense that can be C0-approximated, but an exact solution...