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Designing Automated Market Makers with Adaptive Liquidity


There is a recent surge on the design of automated market makers for securities markets over a finite outcome space, among which is a growing interest in finding automated market makers that have sensitive liquidity. That is, the class of market makers that could adjust their liquidity levels according to market activities. Towards this goal, we first give a formal definition of liquidity

adaptation,. that captures this intuition. Then, building on the ideas from \cite{ACV11,ACV12} and \cite{OS11}, we introduce a framework for the design of duality-based marker makers that enjoy liquidity adaptation as well as other desired properties. We will show that in return for liquidity adaptation, we must trade off information accuracy. A detailed discussion about this trade-off then follows. We will also define asymptotic profit rate that represent the ability of the market to make a profit in a long run. Finally we discuss the design of \emph{optimal market} that maximize worst case liquidity level given information accuracy and profit rate requirements.

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