Empirical Estimates of Stochastic Systems to Measure the Wealth of Corporate Investors

Financial-market dynamics are inherently uncertain, and stochastic differential equations provide a natural framework for assessing the evolution of investment wealth under such conditions. This study formulates two stochastic systems for measuring the wealth of corporate investors by incorporating expected stock returns, intrinsic growth rates, interest-rate parameters, volatility, periodic effects, and random market fluctuations. The systems are solved analytically through Itô's lemma after logarithmic transformation of the wealth processes, yielding explicit expressions for the fourth and fifth corporate investors. For the fourth corporate investor, the stochastic wealth process is expressed as
$$
V_4(t)=V_{40}\exp\left[\left(\mu\alpha_4-\beta_4-\frac{1}{2}\sigma^2\right)t+\sigma W_t^4\right],
$$
while the corresponding wealth process for the fifth corporate investor is
$$
V_5(t)=V_{50}\exp\left[\left(K\tanh(\alpha_5)-\beta_5-\frac{1}{2}\sigma^2\right)t+\sigma W_t^5\right].
$$
Numerical evaluations are used to examine the effects of intrinsic growth, interest rates, and stock volatility on portfolio values. The results show that increases in intrinsic growth rates generally increase investor wealth, whereas higher interest-rate parameters reduce wealth. Increased volatility lowers wealth under the non-periodic specification and makes wealth more sensitive to market fluctuations when periodic effects are incorporated. Surface-view representations further illustrate the response of investor wealth to changes in the principal model parameters. The findings provide a quantitative basis for corporate investment decisions under time-varying and uncertain market conditions and suggest that stochastic delay and periodic extensions may offer useful directions for subsequent research.