Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets
This paper introduces a rigorous theoretical framework for optimal market making in zero-fee perpetual futures markets, modeling the problem as a stochastic optimal control problem with adaptive spreads and hedging. It contributes a PnL decomposition theorem, HJB equation, High-APY regime theorems, and more. Numerical analysis reveals phase transitions between profitable and unprofitable regimes.
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[Submitted on 5 Apr 2026]
Title:Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets
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Abstract:We develop a rigorous theoretical framework for optimal market making in perpetual futures markets with zero maker fees. We model the market maker's problem as a stochastic optimal control problem on a filtered probability space, where the controls are adaptive bid-ask spreads and inventory hedging decisions across two exchanges. Our contributions include: (i) a PnL decomposition theorem separating revenue into spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure; (ii) the Hamilton-Jacobi-Bellman equation for the joint spread-inventory-hedging control problem under CARA utility with a verification theorem; (iii) High-APY Regime Theorems characterizing profitable regions via five dimensionless parameters, culminating in a Master APY Formula; (iv) analysis of zero-fee economics on decentralized perpetual exchanges with optimal entry-exit thresholds; (v) optimal cross-exchange hedging policies with funding rate dynamics and a hedge regime trichotomy; (vi) a robustness margin quantifying parameter uncertainty tolerance; (vii) exponential drawdown probability bounds and a universal APY-VaR identity; (viii) ergodic inventory distribution under optimal control with Bayesian adaptive estimation; (ix) Kelly-optimal leverage with ruin boundaries; and (x) multi-pair portfolio allocation with diversification saturation results. Numerical analysis with twenty-three figures reveals phase transitions between profitable and unprofitable regimes. Our framework unifies and extends the Avellaneda-Stoikov, Gueant-Lehalle-Fernandez-Tapia, and Glosten-Milgrom paradigms for modern decentralized venue microstructure.
Comments: 42 pages, 23 figures
Subjects:
Artificial Intelligence (cs.AI)
MSC classes: 91G10, 93E20, 60J60
Cite as: arXiv:2607.11888 [cs.AI]
(or arXiv:2607.11888v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2607.11888
arXiv-issued DOI via DataCite
Submission history
From: Minmin Zeng [view email] [v1] Sun, 5 Apr 2026 07:21:54 UTC (1,463 KB)
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