Paper proposes stochastic control framework for zero-fee perpetual futures market making

A new arXiv preprint develops a theoretical framework for optimal market making in perpetual futures markets with zero maker fees, framing the market maker’s problem as a stochastic optimal control problem on a filtered probability space. The controls include adaptive bid-ask spreads and inventory hedging decisions executed across two exchanges.

The authors contribute a profit-and-loss decomposition theorem that separates revenue into spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure. They derive the Hamilton–Jacobi–Bellman equation for the joint spread–inventory–hedging control problem under constant absolute risk aversion (CARA) utility, including a verification theorem.

The paper introduces High-APY Regime Theorems that characterize profitable regions via five dimensionless parameters and culminates in a Master APY Formula. It also analyzes zero-fee economics on decentralized perpetual exchanges, including optimal entry–exit thresholds, and derives optimal cross-exchange hedging policies under funding rate dynamics.

Additional results include a robustness margin quantifying tolerance to parameter uncertainty, exponential drawdown probability bounds, a universal APY–VaR identity, and ergodic inventory distributions under optimal control with Bayesian adaptive estimation. The authors also derive Kelly-optimal leverage with ruin boundaries and multi-pair portfolio allocation with diversification saturation results.

Numerical analysis with twenty-three figures is reported to reveal phase transitions between profitable and unprofitable regimes. The framework unifies and extends prior paradigms by Avellaneda–Stoikov, Gueant–Lehalle–Fernandez–Tapia, and Glosten–Milgrom to modern decentralized venue microstructure.