Optimal Design of Automated Market Makers on Decentralized Exchanges

Automated market makers are a popular mechanism used on decentralized exchange, through which users trade assets with each other directly and automatically through a liquidity pool and a fixed pricing function. The liquidity provider contributes to the liquidity pool by supplying assets to the pool, and in return, they earn trading fees from investors who trade in the pool. We propose a model of optimal liquidity provision in which a risk-averse liquidity provider decides the amount of wealth she would invest in the decentralized market to provide liquidity in a two-asset pool, trade in a centralized market, and consume in multiple periods. We derive the liquidity provider's optimal strategy and the optimal design of the automated market maker that maximizes the liquidity provider's utility. We find that the optimal unit trading fee increases in the volatility of the fundamental exchange rate of the two assets. We also find that the optimal pricing function is chosen to make the asset allocation in the liquidity pool efficient for the liquidity provider.