This study develops a stochastic model for revenue-based loan repayment under uncertain income dynamics. Unlike classical deterministic loan models, repayments are linked to stochastic revenue modeled using geometric Brownian motion. Using stochastic differential equations and Itˆo calculus, the repayment dynamics are derived and evaluated under both real-world and riskneutral measures. Monte Carlo simulation is employed to estimate loan values under varying levels of volatility and revenue frequency. Results show that valuation remains stable under low volatility, while high volatility introduces significant variation. Increasing revenue frequency improves model accuracy. The model also ensures feasibility by maintaining repayment below revenue levels. These findings demonstrate that stochastic repayment models provide a flexible and realistic alternative to traditional loan systems.
