This paper develops a continuous-time model for expiration-sensitive products to jointly determine optimal dynamic pricing, advertising investment, and inventory decisions under trade-credit financing. Demand depends on both selling price and advertising-generated goodwill, with goodwill following Nerlove-Arrow dynamics, whereas inventory availability is subject to sales depletion and age-dependent deterioration over time. The trade-credit mechanism introduces regime-switching dynamics based on the relationship between the credit period and the replenishment cycle, leading to a hybrid optimal control problem analyzed using Pontryagin's Maximum Principle. A post-solution approximation of the goodwill trajectory is proposed that preserves the structure of the original optimality conditions while providing semi-closed-form expressions for the optimal policies. Numerical experiments demonstrate that the approximation closely reproduces the exact optimal trajectories and objective values. The results further show that trade credit enhances retailer profitability by relaxing liquidity constraints, thereby enabling lower inventory levels, stronger advertising investment, smoother pricing policies, and higher goodwill, particularly for products with longer expiration periods. The proposed framework provides a decision-support tool for jointly coordinating operational, marketing, and financial decisions in expiration-sensitive supply chains.
