A Technique to Solve a Parabolic Equation by Point Symmetries that Incorporate Initial Data
Year: 2025
Type: article
Abstract: In this paper, we show how transformation techniques coupled with a convolution integral can be used to solve a generalised option-pricing model, including the Black–Scholes model. Such equations are parabolic and the special convolutions are extremely involved as they arise from an initial value problem. New symmetries are derived to obtain solutions through an application of the invariant surface condition. The main outcome is that the point symmetries are effective in producing exact solutions that satisfy a given initial condition, such as those represented by a call-option.
Authors: Sameerah Jamal, Rivoningo Maphanga
Institution: University of the Witwatersrand
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4408055139