Portfolio management is a dynamic decision-making problem characterized by uncertainty, evolving asset states, competing risk–return objectives, and changing market conditions. This research develops an integrated stochastic and optimization framework for modelling financial growth and formulating investment policies by representing a portfolio as a dynamic compartmental system in which risky and non-risky assets undergo stochastic growth, loss, transformation, and migration. Univariate and bivariate birth–death and migration processes, together with Markov and hidden-state modelling perspectives, are employed to characterize the probabilistic evolution and interactions of portfolio components.

The proposed framework systematically connects stochastic process modelling, probability analysis, statistical inference, nonlinear optimization, computational analysis, and decision support. Difference and differential equations are developed to describe portfolio dynamics, while probability-generating functions and moment-based methods are used to derive expectations, variances, covariances, and related measures under transient and steady-state conditions. These statistical characteristics subsequently serve as inputs to stochastic optimization models that address alternative investment objectives, including risk control, volatility management, portfolio diversification, and the determination of appropriate investment policy parameters.

Computational experimentation and sensitivity analysis are incorporated to examine the effects of growth, loss, and transformation parameters on portfolio behavior, using real-world financial data to ground empirical exploration and model validation. The resulting framework provides a pathway from uncertainty modelling to quantitative risk assessment, prescriptive optimization, and intelligent decision support. The research is intended to stimulate interdisciplinary collaboration across Statistics, Stochastic Processes, Mathematical Finance, Operations Research, Optimization, Data Science, and Computational Modelling, with potential applications in real-data validation, software development, joint publications, and future research on scalable stochastic decision-support systems for contemporary financial management.