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The classical Heston model does not consider no long-term dependence of asset, and the financial empirical analysis proves that it can not describe the real situation of assets well. In this article, the mixed Gaussian Heston model is established and stocks data are analyzed. Firstly, the existence and uniqueness of the solution and the properties of the p-order moment of the solution are discussed, respectively. Secondly, the unknown parameters in the model are estimated and the sensitivity analysis are carried out. The actual data of three stocks are used to compare the price path satisfied by Heston model and mixed Gaussian Heston model with the real path. It shows that the mixed Gaussian Heston model can describe the asset price better than the Heston model.vvv
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This paper mainly considers the problem of heteroscedasticity test for partial linear EV model with missing response variables. First, use the completely observed data to estimate the unknown parameters and smooth function of the model, and then use the regression method to fill in the missing data. Then, the empirical likelihood ratio statistic for testing the heteroscedasticity of the random error of the model is established, and it is proved that the statistic asymptotically
obeys the chi-square distribution. Finally, the nature of the limited sample of the test under different missing probabilities is studied through numerical simulation, and the partial linear EV model is used in the case analysis to test the missing data for heteroscedasticity.
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Reinsurance is an effective risk management strategy, which plays an important role in the insurance industry. Under the principle of expected premium, this paper considers the risk of both the insurer and the reinsurer. Taking the convex combination of the VaR value of the total loss of each reinsurance party as the objective function, the theoretical solution of the optimal proportion coefficient and the optimal retention in the mixed reinsurance are obtained. In addition, the
various situations of the optimal solution are discussed and analyzed, which provides the decision basis for the risk management of the insurance company.
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{In this paper, we propose empirical likelihood method for parameter hypothesis test in short memory time series models. In practice, we may pay attention to not only the significance of all the parameters, but also the significance of some parameter in the models. So we construct different test statistics in these two situations, which are both shown to follow chi-square distributions asymptotically. In addition, our simulations investigate the power function for testing the concerned parameters and verify the validity of the proposed testing procedure.
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Regression models are traditionally estimated using the least square estimation (LSE) method which may result in non-robust parameter estimates when data includes non-normal feature or outliers. Compared to LSE approach, composite quantile regression (CQR) can provide more robust estimation results even suffering non-normal errors or outliers. Based on a composite asymmetric Laplace distribution (CALD), the weighted composite quantile regression (WCQR) can be treated in the Bayesian framework. Regularization methods have been verified to be very effective for high-dimensional sparse regression models in that
it can simultaneously conduct variable selection and parameters estimation. In this paper, we combine Bayesian LASSO regularization methods with WCQR to fit linear regression models. Bayesian LASSO-regularized hierarchical models of WCQR are constructed and the conditional posterior distributions of all unknown parameters are derived to conduct statistical inference. Finally, the developed methods are illustrated by Monte Carlo simulations and a real data analysis.
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Variable selection is of significant importance for classification and regression tasks in machine learning and statistical applications where both predictability and explainability are needed. In this paper, a Copula Entropy (CE) based method for variable selection which use CE based ranks to select variables is proposed. The method is both model-free and tuning-free. Comparison experiments between the proposed method and traditional variable selection methods, such as distance correlation, Hilbert-Schmidt independence criterion, stepwise selection, regularized generalized linear models and adaptive LASSO, were conducted on
the UCI heart disease data. Experimental results show that CE based method can select the `right' variables out more effectively and derive better interpretable results than traditional methods do without sacrificing accuracy performance. It is believed that CE based variable selection can help to build more explainable models.
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In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria. These results are established by introducing some restriction on the regularity of the optimal controls and by developing a new compactification method for continuous-time Markov decision processes, which is originally used to solve the optimal control problem for diffusion processes.
