A New Mathematical Blueprint for Market Making in Crypto's Perpetual Futures

Minmin Zeng's latest arXiv submission tackles a question that has quietly frustrated quantitative traders since perpetual futures became crypto's dominant derivatives product: when does market making on these contracts actually turn a profit, and when does it quietly bleed capital?

The 42-page paper, filed to arXiv (2607.11888) and listed under the Artificial Intelligence (cs.AI) category, builds a stochastic optimal control framework specifically designed for market makers operating perpetual futures across two exchanges simultaneously. Rather than treating spread-setting and inventory management as separate problems, the work fuses bid-ask spread adjustment, inventory hedging, and cross-exchange positioning into a single unified control problem, one that a market maker must solve continuously as prices and order flow evolve.

The Core Machinery

At the heart of the paper is a Hamilton-Jacobi-Bellman equation constructed for what Zeng calls spread-inventory-hedging control, evaluated under CARA (constant absolute risk aversion) utility. This isn't just a modeling exercise: the paper backs the equation with a verification theorem, giving the framework a rigorous mathematical guarantee that the derived optimal strategy is genuinely optimal rather than merely a plausible heuristic.

The practical payoff for practitioners lies in the PnL decomposition theorem. It breaks a market maker's returns into five distinct components: spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure. That last term matters enormously in perpetual futures specifically, since funding rates (the periodic payments exchanged between long and short positions to keep perpetual prices tethered to spot) can silently erode or inflate a market maker's returns depending on positioning.

Mapping Where Profit Actually Lives

Perhaps the most immediately useful contribution is what the paper terms the High-APY Regime Theorems, paired with a Master APY Formula expressed through five dimensionless parameters. Together, these tools let a trader or fund characterize, analytically rather than by brute-force backtesting, the precise combinations of spread width, volatility, funding conditions, and inventory limits under which a market-making strategy sits in a profitable regime.

The paper's 23 figures reinforce this with numerical analysis illustrating sharp phase transitions between profitable and unprofitable operating regions. That framing, borrowed from statistical physics, suggests the boundary between a viable and a loss-making strategy isn't gradual but can flip abruptly as parameters cross critical thresholds, a finding with real consequences for risk managers setting operational limits.

While the paper's classification under cs.AI might seem unusual for what is fundamentally a quantitative finance and stochastic control contribution, it reflects arXiv's increasingly blurred boundaries between algorithmic trading research and the broader computational methods community. For quant desks and crypto-native trading firms, the value here isn't a trading signal, but a rigorous analytical lens for understanding exactly why perpetual futures market making succeeds or fails.