Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0929.35006
Gazizov, R.K.; Ibragimov, N.H.
Lie symmetry analysis of differential equations in finance. (English)
[J] Nonlinear Dyn. 17, No.4, 387-407 (1998). ISSN 0924-090X; ISSN 1573-269X/e

The Black-Schole equation $u_t+\frac{1}{2} A^2x^2u_{xx}+ Bxu_x-Cu=0$ and Jacobs-Jones equation $u_t=\frac{1}{2} A^2x^2u_{xx}+ ABCxyu_{xy}+ \frac{1}{2}B^2y^2u_{yy} +(Dx\ln\frac{y}{x}- Ex^{3/2})u_x+ (Fy\ln\frac{G}{y}- Hyx^{1/2})u_y-xu$ are investigated in this paper. For the equations, algebras of classical symmetries are calculated; particular solutions are found with the help of symmetries. The most general transformation of the Black-Schole equation to the heat equation is obtained. The fundamental solution of the Cauchy problem for this equation is found.
[V.A.Yumaguzhin (Pereslavl'-Zalesskij)]

MSC 2000:: *35A30 Geometric theory for PDE, transformations
91B24 Price theory and market structure
58J70 Invariance and symmetry properties

Keywords: fundamental solution of the Cauchy problem; Lie group classification and symmetry analysis; group theoretical modeling; invariant solution; Black-Schole equation; Jacobs-Jones equation; algebras of classical symmetries

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]