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Accelerated genetic algorithm solution of linear black-schole equation
This paper introduced a new accelerated Genetic Algorithms (GAs) method to find a numerical solutions of stochastic Partial differential equations driven by space-time white nose wiener process . The numerical scheme is based on a representation of the solution of the equation involving a stochastic part arising from the noise and a deterministic partial differential equation . By using Doss-Sussmann transformation that enables us to work with a partial differential equation instead of the stochastic partial differential equation. Then compare these solutions obtained by our method with saul'yev method and deterministic solution.
In this research, the development of a fast numerical method was performed in order to solve the Option Pricing problems governed by the Black-Scholes equation using an accelerated genetic algorithm method. Where the Black-Scholes equation is a well known partial differential equation in financial mathematics. A discussion of the solutions was introduced for the linear Black-Scholes model with the European options (Call and Put) analytically and numerically ,with and without transformation to heat equation .Comparisons of the presented approximation solutions of these models with the exact solution were achieved.