Asian Journal of Pure and Applied Mathematics

This paper applies a two model approach an exponential-decay and exponential growth Geometric Brownian Motion (GBM) framework. The two stochastic systems were modified to model the impact of shocks, reversion and capture to \(\mu-k\) where k represents the speed of decay toward equilibrium. The two models were solved by adopting the method of Ito’s where closed form solutions were obtained. From the stochastic analysis of the problems, results show as follows (i) Brownian motion paths are first presented to illustrate the source of randomness during period of trading.(ii) Sample price path of decay model show how assets that start together and diverge under decay and volatility. (iii)Sensitivity analysis demonstrates that the relationship between k and \(\mu\) determines whether valuations grow, remain stable, or decay exponentially. (iv) The sample price path of growth model demonstrates how the same growth rate can produce both upward and downward trajectories depending on shock realizations. (v) Its sensitivity analysis conducted showed the effect of k on path dispersion. This framework provides insight into decision making in Nigerian banking sector.