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 2014 Vol.30 Issue.6,Published 2014-12-27 article
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 561 The Random Parameters AACD Models and Their Geometric Ergodicity Miao Junhong, Shen Jun This paper proposes a new type of random parameters AACD (RPAACD) models, which extends the AACD model. Depending on the state of the price process, the RPAACD models seem to be a valuable alternative to existing approaches and have the better overall performance. We give the transition probability of the process. Moreover by employing the transition probability, we obtain the probability properties of the RPACD model. 2014 Vol. 30 (6): 561-569 [Abstract] ( 758 ) [HTML 1KB] [ PDF 372KB] ( 1236 )
 570 New Bernstein's Inequalities for Dependent Observations and Applications to Learning Theory Zou Bin, Tang Yuanyan, Li Luoqing, Xu Jie The classical concentration inequalities deal with the deviations of functions of independent and identically distributed (i.i.d.) random variables from their expectation and these inequalities have numerous important applications in statistics and machine learning theory. In this paper we go far beyond this classical framework by establish two new Bernstein type concentration inequalities for $\fn_jvn \100dpi \inline \beta$-mixing sequence and uniformly ergodic Markov chains. As the applications of the Bernstein's inequalities, we also obtain the bounds on the rate of uniform deviations of empirical risk minimization (ERM) algorithms based on $\fn_jvn \100dpi \inline \beta$-mixing observations. 2014 Vol. 30 (6): 570-584 [Abstract] ( 1168 ) [HTML 1KB] [ PDF 479KB] ( 1307 )
 585 Pricing Forward Starting Call Options under a Markov-Modulated Jump Diffusion Process The pricing problem of forward starting call options under a Markov-modulated jump diffusion process is studied. Under the assumption that the dynamics of risky asset follows a Markov-modulated jump diffusion process, the explicit analytical formula of forward starting call options is obtained by the change of measure and no arbitrage pricing theory. Moreover, the numerical results of option value are provided by the Monte Carlo method, and the value of forward starting call options is compared when the risky asset satisfies different financial models. 2014 Vol. 30 (6): 585-597 [Abstract] ( 728 ) [HTML 1KB] [ PDF 574KB] ( 978 )
 598 An Imputation Method for Missing Data in Compositional Based on Epanechnikov Kernel Zhang Xiaoqin, Kang Ju, Jing Wenjun Kernel function method has been successfully used for the estimation of a variety of function. By using the kernel function theory, an imputation method based on Epanechnikov kernel and its modification were proposed to solve the problem that missing data in compositional caused the failures of existing statistical methods and the k-nearest imputation didn't consider the different contributions of the k nearest samples when it used them to estimated the missing data. The experimental results illustrate that the modified imputation method based on Epanechnikov kernel get a more accurate estimation than k-nearest imputation for compositional data. 2014 Vol. 30 (6): 598-606 [Abstract] ( 691 ) [HTML 1KB] [ PDF 512KB] ( 1005 )
 607 The Comparison of Causal Effect Estimation Methods at Missing at Random Han Kaishan When the dependent variable is missing at random, the paper first proposes the four causal effect estimation methods: propensity scores weighted method (PW), improved propensity score weighted method (IPW), augmented propensity weighted estimator (AIPW), regression estimator (REG) and proves the unbiasedness and consistency of the four methods. The paper also proves that AIPW method is double robustness. The four methods are compared when the missing ratio is in different level. It is illuminated that AIPW is more precise and more efficient than other methods. Finally, the causal effect of the American academy of child and adolescent welfare survey data is estimated with the four methods and the results are reached that children accept drug intervention service show no more serious behavior problems than the children who don't accept drug abuse services. 2014 Vol. 30 (6): 607-619 [Abstract] ( 726 ) [HTML 1KB] [ PDF 448KB] ( 1102 )
 620 Pricing Options under Two-Factor Markov-Modulated Stochastic Volatility Models Fan Kun In this paper, we investigate the valuation of European-style call options under an extended two-factor Markov-modulated stochastic volatility model, where the first stochastic volatility component is driven by a mean-reversion square-root process and the second stochastic volatility component is modulated by a continuous-time, finite-state Markov chain. The inverse Fourier transform is adopted to obtain analytical pricing formulae. Numerical examples are given to illustrate the discretization of the pricing formulae and the implementation of our model. 2014 Vol. 30 (6): 620-630 [Abstract] ( 634 ) [HTML 1KB] [ PDF 394KB] ( 1431 )
 631 Local Weighted Composite Quantile Estimating for Varying Coefficient Models Xie Qichang, Lv Xiumei A generalization of classical linear models is varying coefficient models, which offer a flexible approach to modeling nonlinearity between covariates. A method of local weighted composite quantile regression is suggested to estimate the coefficient functions. The local Bahadur representation of the local estimator is derived and the asymptotic normality of the resulting estimator is established. Comparing to the local least squares estimator, the asymptotic relative efficiency is examined for the local weighted composite quantile estimator. Both theoretical analysis and numerical simulations reveal that the local weighted composite quantile estimator can obtain more efficient than the local least squares estimator for various non-normal errors. In the normal error case, the local weighted composite quantile estimator is almost as efficient as the local least squares estimator. Monte Carlo results are consistent with our theoretical findings. An empirical application demonstrates the potential of the proposed method. 2014 Vol. 30 (6): 631-650 [Abstract] ( 759 ) [HTML 1KB] [ PDF 1611KB] ( 1022 )
 651 The Estimation of Accelerated Failure Time Model with Right-Censored Data Deng Wenli, Zhang Tingting, Zhang Riquan The accelerated failure time model provides a natural formulation of the effects of covariates on the failure time variable. The presence of censoring poses major challenges in the semi-parametric analysis. The existing semi-parametric estimators are computationally intractable. In this article we propose an unbiased transformation for the potential censored response variable, thus least square estimators of regression parameters can be gotten easily. The resulting estimators are consistent and asymptotically normal. Based on these, we can get a strongly consistent K-M estimator for the distribution of random error. Extensive simulation studies show that the asymptotic approximations are accurate in practical situations. 2014 Vol. 30 (6): 651-660 [Abstract] ( 840 ) [HTML 1KB] [ PDF 390KB] ( 1259 )
 661 The Optimal Dividend and Capital Injection Strategies in the Classical Risk Model with Randomized Observation Periods Wang Cuilian, Liu Xiao, Xu Lin This paper considers the optimal dividend and capital injection strategies in the classical risk model with randomized observation periods. Assume that ruin is prohibited. We aim to maximise the expected discounted dividend payments minus the expected penalised discounted capital injections. We derive the associated Hamilton-Jacobi-Bellman (HJB) equation and prove the verification theorem. The optimal control strategy and the optimal value function are obtained under the assumption that the claim sizes are exponentially distributed. 2014 Vol. 30 (6): 661-672 [Abstract] ( 662 ) [HTML 1KB] [ PDF 389KB] ( 1328 )

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