# American Institute of Mathematical Sciences

April  2012, 8(2): 343-362. doi: 10.3934/jimo.2012.8.343

## Robust portfolio selection with a combined WCVaR and factor model

 1 Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

Received  March 2011 Revised  August 2011 Published  April 2012

In this paper, a portfolio selection model with a combined Worst-Case Conditional Value-at-Risk (WCVaR) and Multi-Factor Model is proposed. It is shown that the probability distributions in the definition of WCVaR can be determined by specifying the mean vectors under the assumption of multivariate normal distribution with a fixed variance-covariance matrix. The WCVaR minimization problem is then reformulated as a linear programming problem. In our numerical experiments, to compare the proposed model with the traditional mean variance model, we solve the two models using the real market data and present the efficient frontiers to illustrate the difference. The comparison reveals that the WCVaR minimization model is more robust than the traditional one in a market recession period and it can be used in a long-term investment.
Citation: Ke Ruan, Masao Fukushima. Robust portfolio selection with a combined WCVaR and factor model. Journal of Industrial & Management Optimization, 2012, 8 (2) : 343-362. doi: 10.3934/jimo.2012.8.343
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