Application of Stochastic Models for Capital Market Investments: Additive Effects Analysis
Abstract
Accurate estimation of asset value changes in capital markets is fundamental to informed investment decision-making, particularly in highly volatile sectors. While stochastic models such as Geometric Brownian Motion (GBM), Jump Diffusion, and stochastic volatility models have been widely applied to capture price dynamics, these approaches do not incorporate time dependent delay mechanisms that reflect realistic investor behaviour such as delayed asset liquidation in anticipation of price appreciation. The systems of stochastic equations were solved adopting Ito’s theorem where explicit solutions for assessing asset values were obtained. Simulations were performed for varying levels of delay parameters and return rates (1.0000 and 2.0000), under constant volatility, to determine whether delayed strategies generate statistically superior financial outcomes in comparison to immediate asset liquidation. Most existing studies model price dynamics using geometric Brownian motion or stochastic volatility models without incorporating delay-dependent mechanisms. The analysis further revealed that an increase in return rates amplifies these gains, confirming that delay and rate of return interaction contribute positively to wealth accumulation. Goodness-of-fit tests using the Kolmogorov–Smirnov (KS) procedure showed that asset values with delay and without delay do not originate from the same distribution at a 1% significance level. This statistical divergence suggests that delay is not only financially advantageous but also structurally alters the stochastic behaviour of asset values, implying higher risk–return sensitivity. Moreover, graphical results corroborated these findings by displaying upward trajectories for delayed assets, contrasted with low or stagnant returns for non-delayed strategies. To this end, the study provided actionable insights for investors, portfolio managers, and policymakers seeking optimal timing strategies to enhance wealth creation in capital markets.