Modulation instability and solitary wave analysis of the Ivancevic option pricing model via Novel mathematical techniques

In academia, financial engineering challenges are very important, and there is an ongoing demand for effective ways to examine and evaluate these models. The new extended direct algebraic approach and the new auxiliary equation method have been used in this study to investigate the analytical solutions of the economically significant model known as the Ivancevic option pricing model (IOPM) in the sense of a new definition of M-truncated derivative. Additionally, we will examine the equation’s modulation instability (MI) using linear stability approach that demonstrates the accuracy and stability of all combined solutions. The analytical method of this model is infrequently observed in the literature, despite the fact that numerous scholars have examined its applicability and feasibility. The regulated Brownian motion associated with a non-linear Schr¨odinger type equation is described by this model. Mathematical approaches are applied to generate the solution to understand the fluctuations in market prices for the proposed model. The reaction of system to pulse propagation is explained through the use of graphical representations in ۲D, contour and ۳D forms. Anticipating suitable parameter values that correspond with the observed data is made possible by these illustrations. The sensitivity analysis predicts the model’s dependence on the initial conditions. The findings of this study indicated that the suggested approaches preserved the physical characteristics present in realistic processes while providing a very dependable and adaptable substitute for problem-solving. Furthermore, we guarantee that all of the results demonstrate that these techniques are a useful mathematical tool for identifying precise solitary wave solutions to nonlinear models that are present in various scientific and technical domains.

کلیدواژه ها:

Ivancevic option pricing model ، M-truncated derivative ، New extended direct algebraic method ، new auxiliary equation method ، Exact solutions ، modulation instability analysis