Max Y. Melnikov, Yuri A. Melnikov
Abstract:
A technique is proposed for the construction of Green's functions for
terminal-boundary value problems of the Black-Scholes equation. The
technique permits an application to a variety of problems that vary by
boundary conditions imposed. This is possible by extension of an approach
that was earlier developed for partial differential equations in applied
mechanics. The technique is based on the method of integral Laplace
transform and the method of variation of parameters. It provides closed form
analytic representations for the constructed Green's functions.
Submitted August 28, 2007. Published November 14, 2007.
Math Subject Classifications: 35K20, 58J35.
Key Words: Black-Scholes equation; Green's function.
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Max Y. Melnikov Labry School of Business and Economics Cumberland University Lebanon, TN 37087, USA email: mmelnikov@cumberland.edu, Phone 615-547-1260 |
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Yuri A. Melnikov Department of Mathematical Sciences Middle Tennessee State University Murfreesboro, TN 37132, USA email: ymelniko@mtsu.edu, Phone 615-898-2844, Fax 615-898-5422 |
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