Algebraic resolution of equations of the Black-Scholes type with arbitrary time-dependent parameters

作者：Tamizhmani K M^*; Krishnakumar K; Leach P G L

来源：Applied Mathematics and Computation, 2014, 247: 115-124.

DOI：10.1016/j.amc.2014.08.087

• Symmetry analysis
• Black-Scholes Equation
• Financial mathematics

We examine various forms of the Black-Scholes Equation using symmetry analysis and consider the standard problem of a terminal condition, namely u(T, x) =U. The models considered are the standard form of the equation to provide a benchmark, the nonhomogeneous form and two variations in which the parameters of the two basic models are explicitly time dependent. We find, subject to some constraints upon the parameters, a remarkable robustness in the results.

• 出版日期2014-11-15