Enyinnaya Ekuma-Okereke, Joseph Thomas Eghwerido, E. Efe-Eyefia, Samuel Zelibe, Stochastic Analysis of the Effect of Asset Prices to a Single Economic Investor, BMSA Volume 17, Bulletin of Mathematical Sciences and Applications (Volume 17)
https://www.scipress.com/BMSA.17.33
Abstract:
    In this paper, we propose a single economic investor whose asset follows a geometric Brownian motion process. Our objective therefore is to obtain the fair price and the present market value of the asset with an infinitely horizon expected discounted investment output. We apply dynamic programming principle to derive the Hamilton Jacobi Bellman (HJB)-equation associated with the problem which is found to be equivalent to the famous Black-Scholes Model under no risk neutrality. In addition, for a complete market under equilibrium, we obtained the value of the present asset with risk neutrality and its fair price.
Keywords:
    Dynamic Programming Principle, Geometric Brownian Motion, Risk Neutrality, Stochastic Control