Price prediction and selling strategy optimization using the Feynman formula differential equations

In the field of e-business, strategic pricing, and competent inventory management are crucial for commerce sustainability. This study explores the stochastic processes application, especially leveraging Ito’s calculus with Feynman–Kac Formula, for optimizing inventory management for sustainable and energy-efficient e-business solutions. We propose a model that particularly formulated a stochastic differential equation to capture the difficulties of product cost dynamics, energy consumption during storage, demand variation, and encompassing factors like market fluctuations. By using Ito’s calculus, we achieve precious insights into the primary price movements that allow for developed decision-making. The basis of this approach relies on the Feynman–Kac formula, which creates an essential link between the product governing dynamics and its final price. We start with defining model parameters, and then capture the dynamics of the asset price evolution by formulating a stochastic differential equation (SDE) and applying Ito’s Rule. Next, solve the Feynman–Kac Equation, and finally simulate asset price paths and estimate the expected payoff. This approach can be functional to e-business circumstances to reveal the optimized selling window for specific price points to guarantee competent inventory management and contribute to a more sustainable e-commerce model.