The project aims to:

• Explore the optimal design of Automated Market Makers (AMMs) — in particular, the optimisation of liquidity providers’ (LPs) payoff
• Analyse how AMM design influences liquidity usage within Decentralized Finance (DeFi), and identify potential optimisation mechanisms

Liquidity provision is a major issue for all financial markets. In equity markets, trading platforms rely on a variety of mechanisms, but limit order books (LOBs) remain dominant. In markets such as corporate bonds or foreign exchange—typically over-the-counter—market makers/dealers provide liquidity by streaming prices or responding to Request for Quotes (RFQs).

In recent years, new automatic liquidity-provision mechanisms have emerged in the crypto-asset space, where transaction prices are determined algorithmically. These systems are known as Automated Market Makers (AMMs). Their core idea is that liquidity providers deposit reserves of two digital assets, and AMM users can perform swaps between these assets as long as post-transaction reserves satisfy a predetermined equation.

This automatic mechanism—particularly through constant-function formulas—has been used for several years by platforms such as Uniswap, Sushiswap, Curve, and Balancer, and now represents a significant share of trading volumes.

These new mechanisms raise numerous theoretical and practical questions that require substantial research. This research effort, very recent, has already begun to take shape. Several questions emerge. From the perspective of an AMM designer, a central issue lies in choosing the appropriate parameters (pricing formula, transaction fees, concentrated liquidity as in Uniswap v3, etc.) to attract liquidity providers—by minimising impermanent loss—while also attracting users seeking efficient execution. An initial academic literature has begun to address these questions.

Although this growing literature is uneven in scientific quality, it offers a relevant starting point for the work of a team of mathematicians and finance researchers within the Research Initiative. The emergence in France of Swaap, the company funding this Research Initiative, guarantees a stimulating environment with strong expertise.

Two main research topics have been identified so far.

1. Optimising the joint payoff of LPs and liquidity through parameter design

Following the literature on LP revenues, initial research will focus on the joint optimisation of LP payoff and liquiditythrough parameter choices.
The price-discovery rule may incorporate external price indicators, raising the issue of oracles. As in any decentralised protocol, one may choose to sacrifice a degree of decentralisation by using oracles to increase efficiency. Pricing rules may also be dynamic rather than static, potentially including conditional mechanisms similar to those in Uniswap v3. More broadly, this research stream will explore the optimal design of AMMs.

2. Smart order routing across AMMs

A second topic concerns smart order routing. A trader wishing to execute a swap through an AMM often has multiple options: many AMM protocols coexist, each operating independently and with different mechanisms. Whether for traders or LPs, this creates a complex set of optimisation problems related to execution quality, yield maximisation, and price impact.

Similar phenomena may even arise within a single AMM protocol that offers several liquidity options (e.g., dual-AMM vs. multi-asset AMM) to both traders and LPs.

Optimising execution and liquidity provision, as well as analysing the implications for protocol design, is also a central objective of this Research Initiative.

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