Asian Journal of Pure and Applied Mathematics

This study introduces a Laplace transform approach to derive analytical solutions for investment portfolios in volatile stock markets, with a focus on the Nigerian context. Traditional models like mean-variance analysis often fail to capture stochastic dynamics, volatility, and time-dependent factors in emerging economies. By formulating systems of second-order differential equations for asset prices and applying Laplace transforms, closed-form solutions incorporating modified Bessel functions are obtained, revealing symmetric properties and normal distributions of asset values. Results from graphical analyses demonstrate how volatility influences gradual price stabilization, maturity parameters reduce short-term fluctuations, and growth rates balance risk-return dynamics. The framework provides robust tools for asset allocation, risk assessment, and forecasting, offering practical implications for investors and policymakers in navigating market uncertainties.