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Absolute Deviation

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Peng Zhang – One of the best experts on this subject based on the ideXlab platform.

  • Multiperiod mean Absolute Deviation uncertain portfolio selection with real constraints
    Soft Computing, 2018
    Co-Authors: Peng Zhang

    Abstract:

    Absolute Deviation is a commonly used risk measure, which has attracted more attentions in portfolio optimization. Most of existing mean—Absolute Deviation models are devoted to stochastic single-period portfolio optimization. However, practical investment decision problems often involve the uncertain dynamic information. Considering transaction costs, borrowing constraints, threshold constraints, cardinality constraints and risk control, we present a novel multiperiod mean Absolute Deviation uncertain portfolio selection model, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. In proposed model, the return rate of asset and the risk are quantified by uncertain expected value and uncertain Absolute Deviation, respectively. Cardinality constraints limit the number of risky assets in the optimal portfolio. Threshold constraints limit the amount of capital to be invested in each asset and prevent very small investments in any asset. Based on uncertainty theories, the model is transformed into a crisp dynamic optimization problem. Because of the transaction costs and cardinality constraints, the multiperiod portfolio selection is a mix integer dynamic optimization problem with path dependence, which is “NP hard” problem that is very difficult to solve. The proposed model is approximated to a mix integer dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy and is proved linearly convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

  • MULTIPERIOD CREDIBILITIC MEAN SEMI-Absolute Deviation PORTFOLIO SELECTION
    Iranian Journal of Fuzzy Systems, 2017
    Co-Authors: Peng Zhang

    Abstract:

    In this paper, we discuss a multiperiod portfolio selection problem with fuzzy returns. We present a new credibilitic multiperiod mean semi- Absolute Deviation portfolio selection with some real factors including transaction costs, borrowing constraints, entropy constraints, threshold constraints and risk control. In the proposed model, we quantify the investment return and risk associated with the return rate on a risky asset by its credibilitic expected value and semi- Absolute Deviation. Since the proposed model is a nonlinear dynamic optimization problem with path dependence, we design a novel forward dynamic programming method to solve it. Finally, we provide a numerical example to demonstrate the performance of the designed algorithm and the application of the proposed model.

  • multiperiod mean Absolute Deviation fuzzy portfolio selection model with risk control and cardinality constraints
    Fuzzy Sets and Systems, 2014
    Co-Authors: Peng Zhang, Weiguo Zhang

    Abstract:

    Abstract This paper considers a multiperiod fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control, in which the returns of assets are characterized by possibilistic mean values. A possibilistic Absolute Deviation is defined as the risk control of portfolio. A new multiperiod mean Absolute Deviation fuzzy portfolio selection model with transaction cost, borrowing constraints, threshold constraints and cardinality constraints is proposed. Based on the theory of possibility measure, the proposed model is transformed into a crisp nonlinear programming problem. Because of the transaction cost, the multiperiod portfolio selection is a dynamic optimization problem with path dependence. The discrete approximate iteration method is designed to obtain the optimal portfolio strategy, and is proved convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

Guolin Liu – One of the best experts on this subject based on the ideXlab platform.

  • least Absolute Deviation based robust support vector regression
    Knowledge Based Systems, 2017
    Co-Authors: Chuanfa Chen, Changqing Yan, Jinyun Guo, Guolin Liu

    Abstract:

    Abstract To suppress the influence of outliers on function estimation, we propose a least Absolute Deviation (LAD)-based robust support vector regression (SVR). Furthermore, an efficient algorithm based on the split-Bregman iteration is introduced to solve the optimization problem of the proposed algorithm. Both artificial and benchmark datasets are employed to compare the performance of the proposed algorithm with those of least squares SVR (LS-SVR), and two weighted versions of LS-SVR with the weight functions of Hampel and Logistic, respectively. Experiments demonstrate the superiority of the proposed algorithm.

Hosik Choi – One of the best experts on this subject based on the ideXlab platform.

  • smoothly clipped Absolute Deviation on high dimensions
    Journal of the American Statistical Association, 2008
    Co-Authors: Yongdai Kim, Hosik Choi

    Abstract:

    The smoothly clipped Absolute Deviation (SCAD) estimator, proposed by Fan and Li, has many desirable properties, including continuity, sparsity, and unbiasedness. The SCAD estimator also has the (asymptotically) oracle property when the dimension of covariates is fixed or diverges more slowly than the sample size. In this article we study the SCAD estimator in high-dimensional settings where the dimension of covariates can be much larger than the sample size. First, we develop an efficient optimization algorithm that is fast and always converges to a local minimum. Second, we prove that the SCAD estimator still has the oracle property on high-dimensional problems. We perform numerical studies to compare the SCAD estimator with the LASSO and SIS–SCAD estimators in terms of prediction accuracy and variable selectivity when the true model is sparse. Through the simulation, we show that the variance estimator of Fan and Li still works well for some limited high-dimensional cases where the true nonzero coeffic…