Belief Propagation Algorithm for Portfolio Optimization Problems

Abstract

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. Mézard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for finding the optimal portfolio with respect to a given return set. In this study, an approximation algorithm based on belief propagation for the portfolio optimization problem is presented using the Bethe free energy formalism, and the consistency of the numerical experimental results of the proposed algorithm with those of replica analysis is confirmed. Furthermore, the conjecture of H. Konno and H. Yamazaki, that the optimal solutions with the absolute deviation model and with the mean-variance model have the same typical behavior, is verified using replica analysis and the belief propagation algorithm.

5 pages, 2 figures, to submit to EPL

References in corpus (4)

• Expectation Propagation for approximate Bayesian inference
• Risk Minimization through Portfolio Replication
• Perceptron capacity revisited: classification ability for correlated patterns
• Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model

Cited by in corpus (7)

• Self-Averaging Property of Minimal Investment Risk of Mean-Variance Model
• Minimal Investment Risk of Portfolio Optimization Problem with Budget and Investment Concentration Constraints
• Replica Analysis for the Duality of the Portfolio Optimization Problem
• Portfolio Optimization Problem with Non-identical Variances of Asset Returns using Statistical Mechanical Informatics
• Replica Approach for Minimal Investment Risk with Cost
• Pythagorean theorem of Sharpe ratio
• Minimal Investment Risk with Cost and Return Constraints: A Replica Analysis