Electron. J. Diff. Eqns., Vol. 2007(2007), No. 153, pp. 1-14.

Construction of Green's functions for the Black-Scholes equation

Max Y. Melnikov, Yuri A. Melnikov

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
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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