Multi-portfolio Optimization: A Potential Game Approach
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.
KeywordsNash Equilibrium Global Constraint Game Problem Potential Game Nash Equilibrium Problem
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- 1.Markovitz, H.: Portfolio selection. Journal of Finance 7(1), 77–91 (1952)Google Scholar
- 2.Markowitz, H.M.: Portfolio selection: Efficient diversification of investments. Wiley (1959)Google Scholar
- 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.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.Yang, Y., Rubio, F., Scutari, G., Palomar, D.: Multi-portfolio optimization: A potential game approach (2011) (in preparation)Google Scholar