This study proposes a robust optimization framework to address the persistent challenges faced by micro and small enterprises (MSEs) in raising capital due to high levels of demand ambiguity. We examine a robust newsvendor model in which the firm has insufficient initial capital and needs to raise capital from an external fund provider. Without knowing the precise demand distribution, both the firm and the fund provider adopt a max–min decision rule based on the mean and variance of the demand. The firm aims to maximize his expected worst-case profit by determining the production quantity, while the fund provider offers equity or loan financing, seeking a fair market-determined return on the contributed capital. We derive the robust production quantity and financing agreements under both equity and loan financing. We show that equity financing attains the system-optimal outcome under distributional ambiguity, and propose a simple formula for the robust interest rate under loan financing. We further generalize our analysis to consider collateral and initial capital, and extend the base model to a robust principal–agent setting where the firm can exert an unobservable effort to influence demand. In the latter case, we show that equity financing outperforms loan financing across a wide range of parameter values, contrary to the existing literature without demand ambiguity. Our analysis offers guidance for practitioners and policymakers seeking effective strategies to promote growth while safeguarding fund providers in the MSE sector.
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