Collateral Liquidations under Order Book Dynamics: A Formal Model for Aave and Compound

Abstract

We develop a rigorous framework for modeling collateral liquidations in decentralized lending protocols such as Aave and Compound. In contrast to earlier approaches based on constant-product market maker (CPM) assumptions, real-world liquidations are executed through order books with finite depth. This introduces price impact, modifies solvency conditions, and reduces safe loan-to-value ratios. We introduce the Aggregate Value Function, defined directly on the order book, and establish its monotonicity, concavity, and quasi-linearity, following the quasi-linear order book framework. Building on these properties, we derive solvency inequalities and explicit formulas for safe leverage. Our model extends CPM-based theory to discrete liquidity environments and provides foundations for risk management and parameter design in lending protocols.