Safety First Portfolio Selection Based On Statistical Learning Theory

The safety first(SF) criterion aims to minimize the probability of disaster that the portfolio return below a certain "disaster" level. Moreover, SF is regarded as the root of value-at-risk(Va R) and conditional value-at-risk(CVa R) which are widely used in portfolio selection. Most of the current researches are based on the foundation that the number of samples tends to be infinity. Unfortunately, this condition is so strict that it cannot be satisfied in financial market. Therefore, the realization of SF criterion based on statistical learning theory is investigated in a more in-depth fashion in this dissertation. By using the theoretical analysis and empirical studies, some existing portfolio optimization models, which aim to implement the SF criterion, are improved. Furthermore, some new portfolio optimization models with better generalization ability are established. These results intend to enrich the study of the SF criterion, while make the SF criterion become the tool that could be referenced in the decision of portfolio optimization in financial market. The main contributions of this dissertation are listed as follows:(1) The SF criterion and the existing portfolio optimization models implementing the SF criterion are analyzed. The minimization of the disaster probability in the SF criterion is reduced to a risk functional minimization problem which has been studied in statistical learning theory. The limitations of the existing portfolio optimization models, especially the impact of the number of the available samples on the generalization ability, have been pointed out in both theory and practice. Moreover, the relation between the portfolio selection based on the SF criterion and the classification problems is discussed, thus find that they can be reduced to the same risk functional minimization problem.(2) Based on the generalization bound in statistical learning theory, a soft margin-based generalization bound on the disaster probability is deduced, and three portfolio optimization models are built to minimize the soft margin-based generalization bound. Moreover, the threeIV portfolio optimization models are analyzed in theory. The generalization bound in statistical learning theory has been applied to implement the SF criterion by other scholars. The three portfolio optimization model absorbs this idea and compensates the defects that the non-convex optimization problem has to be solved. Moreover, the parameter range is discussed, and the iteration grid search(IGS) algorithm is applied into the optimization of the parameter. Experimental results demonstrate that the generalization ability of the proposed portfolio optimization model is better than the smoothed model.(3) Based on the structural risk minimization principle and its direct implement in statistical learning theory, the smoothed model and the 0-1 mixed integral linear program portfolio optimization model are improved. Based on the structural risk minimization principle and its direct implement, a 2-norm constraint is imposed on the original model to establish an improved model, and the impact of the norm constraint on the generalization ability is discussed. Moreover, the parameter range is discussed, while the relation between the improved model with a certain parameter and the original model as well as the equally weight portfolio, thus find that the improved model is a generalization of the original model as well as the equally weight portfolio. Experimental results show that, compared with the original model and the equally weight portfolio, the improved model generally achieves better out-of-sample performance.(4) In consideration with the relation between the portfolio selection based on the SF criterion and the classification problems, two portfolio optimization models based on one class support vector machines and Mahalanobis one class support vector machines are established to implement the SF criterion. Different from the existing portfolio optimization models based on the support vector algorithms, these two models use the assets as the attributes for classification problems, rather than the influential factors to the assets return.Therefore, the portfolio weight vector can be obtained directly by the support vector algorithms. This method can provide a new insight into the applications of the support vector algorithms in portfolio selection. The superiorities of the two portfolio models are verified byexperimental results.