A Stochastic Inventory Model with Trade Credit and Financial Risk under Demand Uncertainty: A Working Capital Optimization Approach

Trade credit is not just a payment convenience; it is a short-term financing tool that reshapes a firm's working capital and exposes it to default risk whenever realized revenue falls short of what is owed. This paper builds a stochastic inventory model that puts ordering decisions and default risk into a single optimization. Demand is a continuous random variable, and repayment capacity is tied to realize revenue through, where the order quantity Q is chosen before demand is observed. Default occurs when revenue net of interest earned during the credit window falls short of the amount owed to the supplier, which makes the default probability endogenous to the order quantity rather than an external parameter. The retailer maximizes expected net financial value after procurement cost, holding cost, interest, and expected default loss. We establish strict concavity of the objective under mild conditions, characterize the unique optimal order quantity in closed form up to a fixed-point condition that bisection resolves in under twenty iterations, and derive signed comparative statics for every contract parameter. A new closed-form decomposition of how the optimal order quantity responds to the credit period yields an exact sufficient condition under which longer credit periods discourage rather than stimulate ordering, revising the standard intuition from the deterministic trade credit literature. The numerical study is calibrated to a stylized emerging-market retailer and then to conditions facing micro and small trading enterprises in Odisha, India, including the credit ceiling and penal interest rate set under the MSMED Act, 2006. Comparisons against the classical and interest-adjusted newsvendor models quantify the value of joint financial-operational modeling, and an elasticity analysis, joint sensitivity surfaces, and a working capital ratio diagnostic give retailers, suppliers, and lenders practical tools for demand-uncertain, capital-constrained trade credit settings. JEL Classification C61; D81; G32; M11.