Three new weak formulations of the problem of American call options valuation

Abstract

© Published under licence by IOP Publishing Ltd. Three new weak formulations of the problem of American call options valuation are given. The first of these is a parabolic obstacle problem in a finite domain. The second is a parabolic variational inequality with a convex and Lipschitz-continuous functional and the last one is a semilinear parabolic equation with a discontinuous spatial operator. All these problems are equivalent - they have the same unique solution. Different formulations can be used both for theoretical research and for constructing numerical methods.