Dynamic Interest Rate Discovery in Decentralized Finance: A Reverse Kelly Automated Market Maker for Risk-Adjusted Lending

Abstract

Decentralized Finance (DeFi) lending protocols currently rely on heuristic, utilization-based bonding curves that mandate severe over-collateralization, systematically excluding under-collateralized assets like corporate invoices. This paper introduces a mathematically optimal pricing mechanism for decentralized credit: the Reverse Kelly Automated Market Maker (rkAMM), the core engine of our proposed lending framework. By inverting the Kelly Criterion, traditionally used for optimal bet sizing, we construct a dynamic interest rate discovery protocol that explicitly prices individual loan risk. The rkAMM ingests real-time Probability of Default (PD) streams from an off-chain Explainable AI oracle and dynamically calculates the exact interest rate required to sustain target liquidity provider (LP) yields. We mathematically derive the Reverse Kelly pricing function ($r = \frac{y + PD}{1 - PD}$), proving its strictly convex superiority over Aave and Compound's static utilization curves in managing capital efficiency. Furthermore, we deploy the rkAMM architecture via Solidity smart contracts, optimizing for gas-efficient 1e18 (WAD) floating-point arithmetic. To ensure decentralized transparency, our simulation infrastructure leverages MLflow for tracking yield hyperparameters, Data Version Control (DVC) linked to DagsHub for versioning Real-World Asset (RWA) data arrays, and localized edge-inference via Ollama (Llama-3) and Hugging Face (FinBERT) for zero-cost predictive modeling. Monte Carlo simulations across 10,000 macroeconomic stress scenarios confirm that the rkAMM maintains protocol solvency and stabilizes LP yields at 12-15\% net of expected credit losses. This work provides the foundational financial engineering required to bridge the \$2 trillion global supply chain finance gap using permissionless blockchain infrastructure.