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Lie symmetry analysis of differential equations in finance. (English) Zbl 0929.35006
The Black-Schole equation u t +1 2A 2 x 2 u xx +Bxu x -Cu=0 and Jacobs-Jones equation u t =1 2A 2 x 2 u xx +ABCxyu xy +1 2B 2 y 2 u yy +(Dxlny x-Ex 3/2 )u x +(FylnG 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.
35A30Geometric theory for PDE, characteristics, transformations
91B24Price theory and market structure
58J70Invariance and symmetry properties