为永续合约市场设计了高收益做市的理论框架，兼顾风险与收益。
Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets
- 构建随机最优控制模型，动态调节报价和对冲策略。
- 提出收益分解公式和年化收益率主公式，揭示盈利边界。
- 适合量化交易员和去中心化交易所设计者参考。
我们为零手续费的永续合约市场构建了一个严谨的理论框架，将做市商问题建模为滤空间上的随机最优控制问题，控制变量包括自适应买卖价差及跨两交易所的头寸对冲决策。贡献包括：(i) 收益分解定理，将利润拆分为价差收入、逆向选择损失、持仓成本、对冲摩擦和资金费率暴露；(ii) 基于CARA效用的联合价差-头寸-对冲控制的哈密顿-雅可比-贝尔曼方程及验证定理；(iii) 高年化收益率区域定理，通过五个无量纲参数刻画盈利区间，导出主年化收益率公式；(iv) 零费经济下去中心化交易所的最优进出阈值分析；(v) 考虑资金费率动态的跨交易所对冲策略及三类对冲状态；(vi) 参数不确定性的鲁棒性容忍度量化；(vii) 暴跌概率的指数界与通用年化收益率-风险价值恒等式；(viii) 在最优控制下库存的遍历分布及贝叶斯自适应估计；(ix) 凯利最优杠杆与破产边界；(x) 多币对组合配置与分散化饱和结果。23幅数值图揭示了盈利与非盈利区间的相变。该框架统一并扩展了阿韦兰达-斯托伊科夫、格恩坦-勒哈尔-费尔南德斯-塔皮亚、格洛斯滕-米尔格罗姆等经典范式，适用于现代去中心化交易微观结构。
原文摘要 · Abstract (English)
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.
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