Optimal Adaptive Market Making for Perpetual Futures Markets

Minmin Zeng, Yi Liu· July 15, 2026 View original

Summary

This paper presents a theoretical framework for optimal market making in zero-fee perpetual futures markets, modeling the problem as a stochastic optimal control. It provides a PnL decomposition, Hamilton-Jacobi-Bellman equation, and theorems for high-APY regimes, extending existing market-making paradigms for modern decentralized exchanges.

A new theoretical framework has been developed for optimal market making, specifically tailored for perpetual futures markets that operate with zero maker fees. The research frames the market maker's challenge as a stochastic optimal control problem, where the key decisions involve adaptively setting bid-ask spreads and managing inventory hedging across multiple exchanges. The framework offers several significant contributions, including a detailed profit and loss (PnL) decomposition that isolates various revenue and cost components such as spread income, adverse selection, and funding rate exposure. It also provides theorems characterizing highly profitable regimes through a "Master APY Formula" and analyzes optimal cross-exchange hedging strategies. This work unifies and expands upon established market-making theories, offering crucial insights for liquidity provision in modern decentralized financial venues.

Why it matters

This framework provides quantitative finance professionals and algorithmic traders with advanced tools and a deeper theoretical understanding to optimize market-making strategies, potentially leading to higher yields and more robust risk management in complex perpetual futures markets.

How to implement this in your domain

  1. 1Study: Analyze the PnL decomposition and High-APY Regime Theorems to refine existing market-making models.
  2. 2Model: Incorporate the stochastic optimal control problem and Hamilton-Jacobi-Bellman equation into quantitative trading algorithms.
  3. 3Optimize: Adjust bid-ask spread and inventory hedging strategies based on the framework's insights into funding rate dynamics and cross-exchange policies.
  4. 4Simulate: Use the framework's principles to simulate and backtest new market-making strategies in perpetual futures.

Who benefits

FinTechQuantitative FinanceCryptocurrencyInvestment BankingAlgorithmic Trading

Key takeaways

  • A new theoretical framework optimizes market making in zero-fee perpetual futures markets.
  • It provides a detailed PnL decomposition for various revenue and cost factors.
  • High-APY regimes are characterized by a "Master APY Formula" and five parameters.
  • The framework offers optimal cross-exchange hedging policies and extends existing market-making theories.

Original post by Minmin Zeng, Yi Liu

"arXiv:2607.11888v1 Announce Type: new Abstract: 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, wh…"

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