Stochastic System Estimates to Assess Corporate Investor Portfolio Value in Stock Markets

Uncertainty in stock-market conditions makes the quantitative assessment of corporate investment portfolios an important problem in financial modelling. This study develops a system of stochastic differential equations for estimating the wealth dynamics of three corporate investors under changing market conditions. The model incorporates expected stock returns, intrinsic growth rates, interest-rate effects, stock-price volatility, and random market fluctuations. The stochastic wealth processes are solved analytically using Itô's lemma, leading to explicit solutions of the general form $$ V_i(t)=V_{i0}\exp\left[\left(\mu\alpha_i-\beta_i-\frac{1}{2}\sigma^2\right)t+\sigma W_i(t)\right],\qquad i=1,2,3. $$ Numerical evaluations are performed to determine the effects of the principal model parameters on corporate-investor portfolio values. The results show that increases in the intrinsic growth-rate parameters $\alpha_i$ are associated with higher terminal wealth, whereas increases in the interest-rate parameters $\beta_i$ reduce portfolio wealth. The volatility parameter $\sigma$ affects both the deterministic Itô correction $-\frac{1}{2}\sigma^2$ and the stochastic component $\sigma W_i(t)$, thereby influencing the distribution and sensitivity of terminal wealth. Under the parameter values considered, the second corporate investor records the largest wealth values among the three investors. The stochastic framework provides a useful mathematical approach for assessing corporate-investor portfolio values and evaluating the effects of key financial parameters under uncertain stock-market conditions.