# Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets

arXiv: https://arxiv.org/abs/2607.11888 · HTML: https://mlsanity.com/paper/2607.11888/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 31 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Builds on (most cited first, 1 of 1)

- [Automated Market Making and Loss-Versus-Rebalancing](https://mlsanity.com/paper/2208.06046/) (2022)

## Abstract (arXiv)

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.