Peter Laurence & Edward Stredulinsky
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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Department of Mathematics, University of Wisconsin
Richland, WI 53581, USA