Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets

Core Contribution: Rigor Meets Quantitative Actionability

This paper (arXiv:2607.11888v1) establishes the first rigorous optimal market making framework for zero-maker-fee perpetual futures markets, formulating the market maker’s problem as a stochastic optimal control problem on a filtered probability space, with controls being adaptive bid-ask spreads and cross-exchange inventory hedging decisions.

Key Technical Results

• PnL Decomposition Theorem: Profit-and-loss is rigorously decomposed into five components — spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure;
• HJB Equation & Verification Theorem: Derives the Hamilton-Jacobi-Bellman equation for the joint spread-inventory-hedging control problem under Constant Absolute Risk Aversion (CARA) utility, accompanied by a full verification theorem;
• High-APY Regime Characterization: Introduces High-APY Regime Theorems that define profitable regions using five dimensionless parameters (e.g., relative volatility ratio, funding rate Sharpe ratio, hedging latency factor), culminating in a closed-form Master APY Formula;
• Zero-Fee Economics Analysis: First systematic analysis of optimal entry-exit thresholds for liquidity provision on decentralized perpetual exchanges operating with zero maker fees;
• Cross-Exchange Hedging Policies: Integrates dynamic funding rate modeling and proposes a hedge regime trichotomy—distinguishing arbitrage-dominated, risk-hedging-dominated, and liquidity-capture-dominated regimes;
• Robustness Margin: Quantifies parameter uncertainty tolerance via a formally defined robustness margin;
• Tail-Risk Control: Provides exponential drawdown probability bounds and a universal AP (asset pricing) approximation.