In this paper, the Black-Sholes equation (BS) has been applied successfully with the Cauchy-Euler method and the method of separation of variables and new analytical solutions have been found. The linear partial differential equation (PDE) transformed to linear ordinary differential equation (ODE) as well. We acquired three types of solutions including hyperbolic, trigonometric and rational solutions. Descriptions of these methods are given and the obtained results reveal that three methods are tools for exploring partial differential models.
Manafian, Jalil and Paknezhad, Mahnaz
Analytical solutions for the Black-Scholes equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 12,
2, Article 13.
Available at: https://digitalcommons.pvamu.edu/aam/vol12/iss2/13