Jump Diffusion Logistic Brownian Motion with Dividend Yielding Asset - Opondo, Mark Ochieng; Oduor, D. B.; Odundo, F. (International Journal of Mathematics And its Applications, 2021)
Jump diffusion processes have been used in modern finance to capture discontinuous behavior in asset pricing. Logistic Brownian motion for asset security prices shows that naturally asset security prices would not usually shoot indefinitely due to the regulating factor that may limit the asset prices. Geometric Brownian motion cannot accurately reflect all behaviors of stock quotation therefore, Merton who was involved in the process of developing the Black-Scholes model came up with Merton jump model superimposed on Geometric Brownian motion without considering the dividend yielding rate of the asset. Therefore in this paper, we have derived the price of dividend yielding asset that follows logistic Brownian motion with jump diffusion process. This study uses the knowledge of Geometric Brownian Motion and logistic Brownian motion with Heaviside’s Cover-up Method to develop the price of dividend yielding asset that follows logistic Brownian motion with jump-diffusion process.
Keywords: Geometric Brownian motion; Logistic Brownian motion; Jump diffusion; Dividend Yielding Asset; Stochastic Process; Wiener Process; Ito’s Process