Optimal transport stress testing and fund-level risk management for DeFi lending against prediction market collateral

In this paper, 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-diffusion 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 establish a formal concentration limit showing that the effective sample size under exponential tilting converges to the number of empirical tail scenarios as views become aggressive, and that support augmentation with synthetic scenarios raises this floor. 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, to our knowledge, has not been developed in the closely related DeFi lending and liquidation literature for prediction-market collateral. Second, we develop a volume-weighted average price walk-the-book liquidation cost model with endogenous horizons derived from observed fill rates and book replenishment dynamics, producing stressed recovery estimates that capture the empirical coupling between adverse price moves and orderbook depletion. Third, we formulate fund-level capital allocation as a linear program over borrower exposures, with concentration limits derived from spectral graph clustering of a market dependency graph combining Hawkes excitation, diffusion correlation, and semantic similarity. Empirical validation on 2,250 comparisons across 250 randomly constructed Polymarket portfolios, five random seeds, and nine stress-view configurations reveals a three-regime structure: under moderate views, optimal transport wins 92% of comparisons with [Formula: see text] higher median effective sample size; under mild views both methods perform well; under extreme views both methods degenerate and the framework activates Filtered Historical Simulation as a robust fallback. Across all regimes, optimal transport wins 79.9% of comparisons, and the results are stable across seeds (78–82% per seed).