  One of the exciting recent developments in decentralized finance (DeFi) has
been the development of decentralized cryptocurrency exchanges that can
autonomously handle conversion between different cryptocurrencies.
Decentralized exchange protocols such as Uniswap, Curve and other types of
Automated Market Makers (AMMs) maintain a liquidity pool (LP) of two or more
assets constrained to maintain at all times a mathematical relation to each
other, defined by a given function or curve. Examples of such functions are the
constant-sum and constant-product AMMs. Existing systems however suffer from
several challenges. They require external arbitrageurs to restore the price of
tokens in the pool to match the market price. Such activities can potentially
drain resources from the liquidity pool. In particular, dramatic market price
changes can result in low liquidity with respect to one or more of the assets
and reduce the total value of the LP. We propose in this work a new approach to
constructing the AMM by proposing the idea of dynamic curves. It utilizes input
from a market price oracle to modify the mathematical relationship between the
assets so that the pool price continuously and automatically adjusts to be
identical to the market price. This approach eliminates arbitrage opportunities
and, as we show through simulations, maintains liquidity in the LP for all
assets and the total value of the LP over a wide range of market prices.
