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Are There AMM Formulas Other than X Y = K Designed to Minimize Impermanent Loss?

Yes, there are alternative AMM designs. For instance, stable-swap AMMs use a formula that behaves like a constant sum (x + y = k) near the peg, offering very low slippage and minimal impermanent loss for assets that are expected to trade near parity, like stablecoins.

Other models, such as concentrated liquidity, allow LPs to allocate capital within a specific price range, which can increase capital efficiency but may increase impermanent loss outside that range.

What Is the Main Risk for a Liquidity Provider Whose Position Is Entirely “Out of Range” in a Concentrated Pool?
What Is a Concentrated Liquidity Pool and How Does It Affect Capital Efficiency?
What Are the Trade-Offs between Capital Efficiency and Impermanent Loss in Different AMM Designs?
What Is a Concentrated Liquidity Model and How Does It Differ from a Standard AMM?