发表机构
tsaftech（tsaftech）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究为零做市商费用的永续期货市场最优做市构建理论框架，将其建模为随机最优控制问题，给出盈亏分解等多项成果，涵盖多方面分析及策略，通过数值分析揭示盈利相变，统一扩展相关范式。
AI 中文摘要
我们为零做市商费用的永续期货市场中的最优做市开发了一个严格的理论框架。我们将做市商的问题建模为一个带过滤概率空间上的随机最优控制问题，其中控制是两个交易所之间的自适应买卖价差和库存对冲决策。我们的贡献包括：（i）一个盈亏分解定理，将收益分为价差收入、逆向选择损失、库存持有成本、对冲摩擦和资金费率风险敞口；（ii）在CARA效用下联合价差 - 库存 - 对冲控制问题的Hamilton - Jacobi - Bellman方程及验证定理；（iii）通过五个无量纲参数表征盈利区域的高年化收益率 regime定理，最终得出主年化收益率公式；（iv）对具有最优进出阈值的去中心化永续交易所的零费用经济学分析；（v）具有资金费率动态和对冲 regime三分法的最优跨交易所对冲策略；（vi）量化参数不确定性容忍度的稳健性边际；（vii）指数回撤概率界和通用年化收益率 - VaR恒等式；（viii）在最优控制下具有贝叶斯自适应估计的遍历库存分布；（ix）具有破产边界的凯利最优杠杆；（x）具有多样化饱和结果的多对投资组合分配。二十三幅图的数值分析揭示了盈利和非盈利 regime之间的相变。我们的框架统一并扩展了现代去中心化交易场所微观结构的Avellaneda - Stoikov、Gueant - Lehalle - Fernandez - Tapia和Glosten - Milgrom范式。
英文摘要
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.
Comments42 pages, 23 figures
