Advertisement

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)

Abstract

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.

Keywords

Cost Function Risk Measure Electronic Commerce Market Maker Coherent Risk Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abernethy, J., Chen, Y., Vaughan, J.W.: An optimization-based framework for automated market-making. In: ACM Conference on Electronic Commerce, EC (2011)Google Scholar
  2. Agrawal, S., Delage, E., Peters, M., Wang, Z., Ye, Y.: A unified framework for dynamic pari-mutuel information market design. In: ACM Conference on Electronic Commerce (EC), pp. 255–264 (2009)Google Scholar
  3. Artzner, P., Delbaen, F., Eber, J., Heath, D.: Coherent measures of risk. Mathematical finance 9(3), 203–228 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  4. Ben-Tal, A., Teboulle, M.: An old-new concept of convex risk measures: The optimized certainty equivalent. Mathematical Finance 17(3), 449–476 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)Google Scholar
  6. Carr, P., Geman, H., Madan, D.: Pricing and hedging in incomplete markets. Journal of Financial Economics 62(1), 131–167 (2001)CrossRefGoogle Scholar
  7. Chen, Y., Pennock, D.M.: A utility framework for bounded-loss market makers. In: Proceedings of the 23rd Annual Conference on Uncertainty in Artificial Intelligence (UAI), pp. 49–56 (2007)Google Scholar
  8. Chen, Y., Vaughan, J.W.: A new understanding of prediction markets via no-regret learning. In: ACM Conference on Electronic Commerce (EC), pp. 189–198 (2010)Google Scholar
  9. Chen, Y., Fortnow, L., Lambert, N., Pennock, D.M., Wortman, J.: Complexity of combinatorial market makers. In: ACM Conference on Electronic Commerce (EC), pp. 190–199 (2008)Google Scholar
  10. Föllmer, H., Schied, A.: Stochastic Finance. Studies in Mathematics, vol. 27. De Gruyter (2002)Google Scholar
  11. Goel, S., Pennock, D., Reeves, D., Yu, C.: Yoopick: a combinatorial sports prediction market. In: Proceedings of the National Conference on Artificial Intelligence (AAAI), pp. 1880–1881 (2008)Google Scholar
  12. Hanson, R.: Combinatorial information market design. Information Systems Frontiers 5(1), 107–119 (2003)MathSciNetCrossRefGoogle Scholar
  13. Hanson, R.: Logarithmic market scoring rules for modular combinatorial information aggregation. Journal of Prediction Markets 1(1), 1–15 (2007)Google Scholar
  14. Markowitz, H.: Portfolio Selection. The Journal of Finance 7(1), 77–91 (1952)Google Scholar
  15. Ostrovsky, M.: Information aggregation in dynamic markets with strategic traders. In: ACM Conference on Electronic Commerce (EC), pp. 253–254 (2009)Google Scholar
  16. Othman, A., Sandholm, T.: Automated market-making in the large: the Gates Hillman prediction market. In: ACM Conference on Electronic Commerce (EC), pp. 367–376 (2010a)Google Scholar
  17. Othman, A., Sandholm, T.: When Do Markets with Simple Agents Fail? In: International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), pp. 865–872 (2010b)Google Scholar
  18. Othman, A., Pennock, D.M., Reeves, D.M., Sandholm, T.: A practical liquidity-sensitive automated market maker. In: ACM Conference on Electronic Commerce (EC), pp. 377–386 (2010)Google Scholar
  19. Pennock, D., Sami, R.: Computational Aspects of Prediction Markets. In: Algorithmic Game Theory, ch. 26, pp. 651–674. Cambridge University Press (2007)Google Scholar
  20. Peters, M., So, A.M.-C., Ye, Y.: Pari-Mutuel Markets: Mechanisms and Performance. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 82–95. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  21. Rockafellar, R.T.: Level sets and continuity of conjugate convex functions. Transactions of the American Mathematical Society 123(1), 46–63 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  22. Rockafellar, R.T.: Convex Analysis. Princeton University Press (1970)Google Scholar
  23. Shalev-Shwartz, S., Singer, Y.: A primal-dual perspective of online learning algorithms. Machine Learning 69, 115–142 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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

Personalised recommendations