2020/09/03 by Yongge Wang, Wang, Yongge · 4 citations
Decision Sciences · Economics, Econometrics and Finance · #91B26 #91Bxx #Complex Systems and Time Series Analysis #Computer Science and Game Theory (cs.GT) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Economics and business #Financial Markets and Investment Strategies #G.2.1 #I.6.3 #J.4 #K.4.4 #Stock Market Forecasting Methods #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.2009.01676
openalex publication_date 2020/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based automated market makers. However, LS-LMSR requires complicated computation (i.e., logarithm and exponentiation) and the cost function curve is concave. In certain DeFi applications, it is preferred to have computationally efficient cost functions with convex curves to conform with the principle of supply and demand. This paper proposes and analyzes constant circle/ellipse based cost functions for automated market makers. The proposed cost functions are computationally efficient (only requires multiplication and square root calculation) and have several advantages over widely deployed constant product cost functions. For example, the proposed market makers are more robust against front-runner (slippage) attacks.