Mixing Constant Sum and Constant Product Market Makers

Two popular forms of automated market makers are constant sum and constant product (CSMM and CPMM respectively). Each has its advantages and disadvantages: CSMMs have stable exchange rates but are vulnerable to arbitrage and can sometimes fail to provide liquidity, while a CPMM can have large impermanent loss due to exchange rate changes but are always able to provide liquidity to participants. A significant amount of work has been done in order to get the best of both constant sum and constant product characteristics. Perhaps most the relevant to this paper is Stableswap, which has an "amplification coefficient" parameter controlling the balance between the two types of behavior [Ego19]. Alternative approaches, such as in [AEC21], involve constructing AMMs using portfolio value functions. However, there is still much work to be done on these fronts. This paper presents multiple novel methods for mixing market makers and demonstrates new tools for designing markets with specific features.