Optimal Transport Stress Testing and Fund-Level Risk Management for DeFi Lending Against Prediction Market Collateral

Abstract

We develop optimal transport stress testing, liquidation cost modeling, and fund-level capital allocation for lending against prediction market collateral. Building on a companion paper that derives first-passage default probabilities under Hawkes-driven jump-discussion dynamics, this paper addresses three challenges that arise when operating the lending protocol at scale. First, we introduce a Wasserstein stress testing methodology that generates synthetic tail scenarios for markets with insufficient historical depth, proving that it achieves strictly higher effective sample sizes than classical Entropy Pooling when the stress region lies outside the empirical support. We further establish an adversarial robustness guarantee: the stressed risk estimate remains bounded even under worst-case perturbations of the empirical distribution within a Wasserstein ball- a formal resilience property that no existing decentralized finance stress testing methodology provides.