This paper explores Automated Market Makers (AMMs) in decentralized finance (DeFi), treating AMMs as black-box systems that convert tokens into prices via exchange functions. It examines various AMM types, including Constant Product, Constant Mean, Constant Sum, Hybrid Function, and Dynamic AMMs, and discusses the impact of concentrated liquidity. The framework provides a geometric representation of AMM operations and highlights similarities and differences across AMM types.
This paper presents a theoretical framework for AMMs, focusing on their role in decentralized finance (DeFi). It introduces an abstract operational model of user-AMM interactions and formalizes fundamental properties of AMMs, including structural and economic aspects. The paper also provides a general solution to the arbitrage problem, a key game-theoretic foundation of AMMs.
This study extends the model of Milionis et al. to analyze the impact of trading fees on arbitrage profits in AMMs. It introduces fees and discrete Poisson block generation times, enabling the computation of the expected instantaneous rate of arbitrage profit in closed form.
This paper proposes a dynamic AMM approach that uses market price oracles to adjust the mathematical relationship between assets in a liquidity pool. By continuously aligning the pool price with the market price, the approach eliminates arbitrage opportunities and enhances liquidity management.
This work introduces dynamic curves for AMMs, leveraging market price oracles to automatically adjust asset relationships in liquidity pools. The approach eliminates the need for external arbitrageurs, maintains liquidity across assets, and preserves the total value of the pool under varying market conditions.
This paper proposes a Dynamic Function Market Maker (DFMM) protocol that addresses inventory risk management through data aggregation and order routing. The DFMM ensures price synchronization with external markets, optimizes inventory risk via arbitrageurs, and incorporates protective buffers to mitigate market volatility. The protocol offers a fully automated, decentralized solution for efficient and stable market making.
A growing number of blockchain-based decentralized exchanges (DEX) have adopted Constant Function Market Makers (CFMMs)—a single-function algorithm to determine the execution price for a trade. We build a model of coexisting exchanges where a centralized exchange (CEX) with the traditional order-book mechanism operates in parallel with a DEX with the CFMM. Traders are either informed or uninformed and endogenously choose their trading venue. We first investigate how the arrival of the CFMM affects an adverse selection cost for market makers and liquidity on both exchanges. Our result indicates that liquidity on the DEX has a positive spillover effect on CEX liquidity. Secondly, we derive a profit function for liquidity providers using the CFMM when there is an asymmetric information problem. As in the traditional market microstructure theory, informed trading imposes an adverse selection cost, while uninformed noise trading adds value to liquidity pools. We analyze the market makers’ equilibrium behavior and endogenize the amount of liquidity supplied via the CFMM.