We have developed a rigorous theoretical framework for optimal market making in perpetual futures markets with zero maker fees. The market maker's problem is modeled as a stochastic optimal control problem on a filtered probability space, with controls being adaptive bid-ask spreads and inventory hedging decisions across two exchanges.
Our contributions include:
- A PnL decomposition theorem that separates revenue into spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure;
- The Hamilton-Jacobi-Bellman equation for the joint spread-inventory-hedging control problem under CARA utility with a verification theorem;
- High-APY Regime Theorems characterizing profitable regions via five dimensionless parameters, culminating in a Master APY Formula;
- Analysis of zero-fee economics on decentralized perpetual exchanges with optimal entry-exit thresholds;
- Optimal cross-exchange hedging policies with funding rate dynamics and a hedge regime trichotomy;
- A robustness margin quantifying parameter uncertainty tolerance;
- Exponential drawdown probability bounds and a universal APY-VaR identity;
- Ergodic inventory distribution under optimal control with Bayesian adaptive estimation;
- Kelly-optimal leverage with ruin boundaries;
- 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.
Blogger's Review: This paper offers profound theoretical insights into market making in perpetual futures, especially in a zero-fee environment. By introducing complex mathematical tools and models, it enables market participants to manage liquidity more precisely while laying a solid foundation for future research.