Enhancing small and medium-sized enterprise factoring: a Stackelberg game-based hybrid pricing model

Constantin Siggelkow and Matthias Scherer

Abstract

In supply chain management and trade credit, buyers of goods or services are often granted a delayed payment goal, and the sellers of the respective goods or services are thus exposed to credit risk. Factoring is a financing decision by which sellers can eliminate this risk from their balance sheet. This service is typically offered on a whole turnover basis; however, most small and medium-sized enterprises prefer financing on a single debt level, and hence adverse selection emerges as an additional source of risk. By employing a game-theoretical min–max approach including a Lévy-frailty ansatz for the multivariate default model, we develop a hybrid linear pricing model for the factor, consisting of a static component and a dynamic component. As part of the derivation, we analyze a two-player Stackelberg game and develop a portfolio optimization problem for the supplier, based on a stochastic gradient descent algorithm, which results in an upper bound for the price. Combining this with a cost-covering condition based on the factor provides the proposed price interval. Finally, we embed into the model the simplest data-rich modeling approach for the dynamic part of our analysis.