Peter Laurence & Edward Stredulinsky
Abstract:
Using the method of symmetrization, we compare the price
of the American option on an index or spread to that of the
solution of a parabolic variational inequality in one spatial
variable. This comparison principle is established for a broad
class of diffusion operators with time and state dependent
coefficients. The purpose is to take a first step towards deriving
symmmetrized problems whose solutions bound solutions of
multidimensional American option problems with variable
coefficients when the computation of the latter lies beyond the
scope of the most powerful numerical methods.
Submitted March 10, 2003. Published July 7, 2003.
Math Subject Classifications: 35K85, 35Q99
Key Words: American options, variational inequalities, free boundary,
parabolic equations, finance, symmetrization,
optimal stopping, rearrangements
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Edward Stredulinsky
Department of Mathematics, University of Wisconsin
Richland, WI 53581, USA
email: estredul@uwc.edu