Group Classification of a Generalized Black--Scholes--Merton Equation

Abstract

The complete group classification of a generalization of the Black-Scholes-Merton model is carried out by making use of the underlying equivalence and additional equivalence transformations. For each non linear case obtained through this classification, invariant solutions are given. To that end, two boundary conditions of financial interest are considered, the terminal and the barrier option conditions.

arXiv comment25 pages

References in corpus (4)

• Group classification of heat conductivity equations with a nonlinear source
• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification
• Enhanced preliminary group classification of a class of generalized diffusion equations

Cited by in corpus (4)

• Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility
• Group Classification of a generalization of the Heath Equation
• Lie symmetries of (1+2) nonautonomous evolution equations in Financial Mathematics
• Group classification and symmetry reductions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy