A theoretical framework for optimal market making in perpetual futures

Providing liquidity on perpetual futures is often advertised with triple digit APY figures and very little fine print. A paper published on arXiv on 15 July, Optimal Adaptive Market Making, tries to put that promise on a formal footing: a stochastic optimal control framework that characterises when market making on perpetuals with zero maker fees is genuinely profitable and when the apparent yield gets eaten by adverse selection and funding.

The setup models the market maker as a control problem on a filtered probability space: at every instant the strategy chooses its bid and ask spreads and how much inventory to hedge on a second exchange, with the goal of maximising a risk averse utility (CARA utility). This is not a popular science piece: it is stochastic control mathematics applied to a problem that until now was mostly discussed in forums and in protocol dashboards.

What the paper contributes

The authors list seven contributions. The most relevant for anyone working in this space:

1. A PnL decomposition theorem that splits results into five components: spread income, adverse selection loss, inventory carrying cost, hedging friction and funding rate exposure. This is the most useful piece in practice, because it turns the classic 'the bot wins or loses' into five separately measurable terms.
2. The Hamilton-Jacobi-Bellman equation for the joint spread, inventory and hedging problem, together with a verification theorem.
3. The High-APY Regime Theorems: conditions, expressed through five dimensionless parameters, that delimit the regions where liquidity provision is profitable, culminating in what the authors call a Master APY Formula.
4. An analysis of zero fee economics on decentralised perpetual exchanges, with optimal entry and exit thresholds.
5. Optimal hedging policies across two exchanges incorporating funding rate dynamics, with a trichotomy of hedging regimes.
6. A robustness margin quantifying how much parameter uncertainty the strategy tolerates before it stops being profitable, along with exponential bounds on drawdown probability.

Why it matters

Context explains the interest. Decentralised derivatives exchanges widely adopted zero maker fees as a tool to attract liquidity, and much of their marketing revolves around striking annualised yields for whoever provides it. That fee model changes the market maker's economics: with no fee income, everything depends on the captured spread, the cost of adverse selection and funding. Having a formal decomposition of those terms, and explicit conditions for when the total is positive, is progress compared with the usual heuristics.

The natural audience is threefold: quantitative teams already running strategies of this kind who want a framework to test their assumptions against, DeFi protocol designers who need to understand which incentive structures keep their liquidity providers viable, and people building automated trading agents, a space where it is increasingly common for an LLM to orchestrate the operation and where having five measurable PnL terms makes it easier to observe what the agent is doing.

The limits

It should be read for what it is: theory. CARA utility is a classic but debatable choice, the theorems depend on assumptions about price and funding dynamics that real markets violate regularly, and the paper does not present, at least in its abstract, empirical validation on market data. It also leaves out operational risks that are decisive in DeFi: smart contract failures, cascading liquidations or oracle manipulation. None of this invalidates the framework, but it does bound its use: it is a measuring stick, not a strategy ready to deploy, and it is certainly not investment advice.

At ElephantPink we read it as a sign of maturity: seeing liquidity provision on perpetuals move from Twitter threads to verification theorems is welcome. The distance between the Master APY Formula and a real profit and loss statement is still large, and that is where the money gets lost.