Minimizing loss probability bounds for portfolio selection

Minimizing loss probability bounds for portfolio selection

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Article ID: iaor201111005
Volume: 217
Issue: 2
Start Page Number: 371
End Page Number: 380
Publication Date: Mar 2012
Journal: European Journal of Operational Research
Authors: ,
Keywords: optimization
Abstract:

In this paper, we derive a portfolio optimization model by minimizing upper and lower bounds of loss probability. These bounds are obtained under a nonparametric assumption of underlying return distribution by modifying the so‐called generalization error bounds for the support vector machine, which has been developed in the field of statistical learning. Based on the bounds, two fractional programs are derived for constructing portfolios, where the numerator of the ratio in the objective includes the value‐at‐risk (VaR) or conditional value‐at‐risk (CVaR) while the denominator is any norm of portfolio vector. Depending on the parameter values in the model, the derived formulations can result in a nonconvex constrained optimization, and an algorithm for dealing with such a case is proposed. Some computational experiments are conducted on real stock market data, demonstrating that the CVaR‐based fractional programming model outperforms the empirical probability minimization.

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