Liquidity-Sensitive Automated Market Makers via Homogeneous Risk Measures

  • Abraham Othman
  • Tuomas Sandholm
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)


Automated market makers are algorithmic agents that provide liquidity in electronic markets. A recent stream of research in automated market making is the design of liquidity-sensitive automated market makers, which are able to adjust their price response to the level of active interest in the market. In this paper, we introduce homogeneous risk measures, the general class of liquidity-sensitive automated market makers, and show that members of this class are (necessarily and sufficiently) the convex conjugates of compact convex sets in the non-negative orthant. We discuss the relation between features of this convex conjugate set and features of the corresponding automated market maker in detail, and prove that it is the curvature of the convex conjugate set that is responsible for implicitly regularizing the price response of the market maker. We use our insights into the dual space to develop a new family of liquidity-sensitive automated market makers with desirable properties.


Cost Function Risk Measure Electronic Commerce Market Maker Coherent Risk Measure 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Abraham Othman
    • 1
  • Tuomas Sandholm
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityUSA

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