Equilibrium Liquidity and Risk Offsetting in Decentralised Markets

Battle Count: 80

Highly relevant to quantitative trading in DeFi and cross-venue strategies. The paper provides actionable insights for LPs managing inventory risk across DEX and CEX venues, quantifies the trade-off between replication aggressiveness and liquidity supply, and characterizes how private information affects market viability. The closed-form solutions for constant product markets (Uniswap) are directly applicable to real DEX protocols. The risk-return decomposition informs position sizing and hedging strategies.

The theoretical framework involves advanced mathematics: FBSDEs, variational methods on Hilbert spaces, Gâteaux differentiability, Lax-Milgram lemma, and differential Riccati equations. However, the closed-form solutions for constant product markets (Proposition 4, Corollary 1) are computationally tractable. The numerical experiments require Monte Carlo simulation of geometric Brownian motion paths and computation of conditional expectations. The transient impact extension (Appendix B) requires solving a 2x2 matrix DRE numerically.

The paper provides complete mathematical proofs in appendices, closed-form solutions for constant product markets, and detailed numerical experiments with specified parameter values (sigma=0.2, T=1, eta=10^-2, psi=10, gamma=0.05, 100,000 simulations with 100 time steps). All model primitives and assumptions are clearly stated. However, no code repository is provided, and the numerical implementation details (e.g., discretization scheme) are not fully specified.