Al-Husain, R.A., & Al-Eideh, B.M.
This study provides a methodology for analyzing price behavior. In place of typical before-and-after regression approaches and time series analysis, a new stochastic diffusion logistic growth price model based on stochastic differential equations is developed that explicitly accounts for price fluctuations and volatility. More specifically, we propose a stochastic version of the logistic growth price model driven by birth and death diffusion processes and random external jumps. Numerical examples for no jumps and the occurrence of jump processes that follow uniform and exponential distributions are considered. This study shows the difference between uniform jumps and exponential jumps, which indicates if the jump processes are affected by growth rates or not, and finally, shows how these differences affect stochastic diffusion logistic growth pricing models. The research indicates that modeling incorporating diffusion processes and random jumps can more accurately depict the volatility of real-life situations. Overall, the findings seem reasonable and are suggested for modeling purposes.