Adaptive Repayment Optimisation for SME Lending: A Stochastic Programming Framework with Generative AI Explanation
John Christiansen
ABSTRACT
This paper introduces the Adaptive Repayment Optimisation Engine (AROE), a novel framework that applies constrained stochastic optimisation to the design of loan repayment schedules for small and medium-sized enterprises (SMEs). Unlike fixed-payment or simple revenue-share structures currently dominant in UK SME lending, AROE decomposes each borrower’s cash flow into trend, seasonality, cyclicality, and idiosyncratic volatility components, then uses Monte Carlo simulation and bounded quasi-Newton optimisation to find repayment schedules that minimise the probability of payment distress subject to lender return constraints. A generative AI explanation layer then translates the mathematical output into natural language rationale serving three audiences: borrower, underwriter, and regulator. We validate the framework on a synthetic universe of 10,000 UK SMEs calibrated to ONS, British Business Bank, and sectoral insolvency data across ten SIC-aligned industry sectors and twelve UK regions. Computational experiments demonstrate that AROE
optimised schedules reduce payment distress probability by a mean of 7.7–26.6% compared to equivalent fixed-payment benchmarks, with the largest improvements observed in sectors exhibiting high revenue volatility and pronounced seasonality (Construction, Accommodation s Food, Retail). We discuss the implications for FCA Consumer Duty compliance, IFRS 6 provisioning, and the commercial viability of the approach as a SaaS product for lending platforms. The framework contributes to the operations research literature by bridging stochastic programming, explainable AI, and financial regulation in a novel application domain.
