Multi-portfolio Optimization: A Potential Game Approach

  • Yang Yang
  • Francisco Rubio
  • Gesualdo Scutari
  • Daniel Palomar
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 75)


Trades from separately managed accounts are usually pooled together for execution and the transaction cost for a given account may depend on the overall level of trading. Multi-portfolio optimization is a technique for combing multiple accounts at the same time, considering their joint effects while adhering to account-specific constraints. In this paper, we model multi-portfolio optimization as a game problem and adopt as a desirable objective the concept of Nash Equilibrium (NE). By formulating the game problem as a potential game, we are able to provide a complete characterization of NE and derive iterative algorithms with a distributed nature and satisfactory convergence property.


Nash Equilibrium Global Constraint Game Problem Potential Game Nash Equilibrium Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Markovitz, H.: Portfolio selection. Journal of Finance 7(1), 77–91 (1952)Google Scholar
  2. 2.
    Markowitz, H.M.: Portfolio selection: Efficient diversification of investments. Wiley (1959)Google Scholar
  3. 3.
    Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14, 124–143 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Nash, J.: Non–cooperative games. Annals of Mathematics 54(2), 286–295 (1951)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    O’Cinneide, C., Scherer, B., Xu, X.: Pooling trades in a quantitative investment process. The Journal of Portfolio Management 32(4), 33–43 (2006)CrossRefGoogle Scholar
  6. 6.
    Pang, J.S., Scutari, G., Palomar, D., Facchinei, F.: Design of cognitive radio systems under temperature-interference constraints: A variational inequality approach. IEEE Transactions on Signal Processing 58(6), 3251–3271 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Savelsbergh, M.W.P., Stubbs, R.A., Vandenbussche, D.: Multiportfolio optimization: A natural next step. In: Guerard, J.B. (ed.) Handbook of Portfolio Construction, pp. 565–581. Springer, US (2010)CrossRefGoogle Scholar
  8. 8.
    Scutari, G., Barbarossa, S., Palomar, D.: Potential games: A framework for vector power control problems with coupled constraints. In: ICASSP 2006 Proceedings, vol. 4 (2006)Google Scholar
  9. 9.
    Scutari, G., Facchinei, F., Pang, J.S., Palomar, D.P.: Monotone communication games: Theory, algorithms, and models. Submitted to IEEE Transactions on nformation Theory (2010)Google Scholar
  10. 10.
    Yang, Y., Rubio, F., Scutari, G., Palomar, D.: Multi-portfolio optimization: A potential game approach (2011) (in preparation)Google Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2012

Authors and Affiliations

  • Yang Yang
    • 1
  • Francisco Rubio
    • 1
  • Gesualdo Scutari
    • 2
  • Daniel Palomar
    • 1
  1. 1.Department of Electronic and Computer EngineeringThe Hong Kong University of Science and TechnologyHong Kong
  2. 2.Department of Electrical EngineeringState University of New York (SUNY)BuffaloUSA

Personalised recommendations