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 2012 Vol.28 Issue.5,Published 2012-10-26 article
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 449 $\fn_jvn \100dpi \inline L^p$ Solutions of BSDEs with Non-Uniformly Lipschitz Coefficients Solutions of BSDEs with Non-Uniformly Lipschitz Coefficients[J]. 应用概率统计, 2012,28(5): 449-456>')" href="#"> Song Li, Liu Qian In this note, we consider a class of backward stochastic differential equations with non-uniformly Lipschitz coefficients. We prove the existence and uniqueness of the $\fn_jvn \100dpi \inline L^p$ solutions with 1
 457 Optimal Control for Utility Portfolio Selection with Liability Chang Hao, Rong Ximin In this paper we use stochastic optimal control theory to investigate a dynamic portfolio selection problem with liability process, in which the liability process is assumed to be a geometric Brownian motion and completely correlated with stock prices. We apply dynamic programming principle to obtain Hamilton-Jacobi-Bellman (HJB) equations for the value function and systematically study the optimal investment strategies for power utility, exponential utility and logarithm utility. Firstly, the explicit expressions of the optimal portfolios for power utility and exponential utility are obtained by applying variable change technique to solve corresponding HJB equations. Secondly, we apply Legendre transform and dual approach to derive the optimal portfolio for logarithm utility. Finally, numerical examples are given to illustrate the results obtained and analyze the effects of the market parameters on the optimal portfolios. 2012 Vol. 28 (5): 457-470 [Abstract] ( 932 ) [HTML 1KB] [ PDF 240KB] ( 1563 )
 471 Moment Complete Convergence for Weighted Sums of $\fn_jvn \100dpi \inline \varphi$-Mixing Random Variables -Mixing Random Variables[J]. 应用概率统计, 2012,28(5): 471-478>')" href="#"> Zhang Zhihua, Chen Pingyan In this paper, the authors discuss the moment complete convergence for weighted sums of $\fn_jvn \100dpi \inline \varphi$-mixing random variables, and obtains the sufficient condition for moment complete convergence of $\fn_jvn \100dpi \inline \varphi$-mixing sequence under some mixing rate condition, which generalize the result of moment complete convergence for weighted sums of i.i.d. random variables to $\fn_jvn \100dpi \inline \varphi$-mixing random variables. 2012 Vol. 28 (5): 471-478 [Abstract] ( 1043 ) [HTML 1KB] [ PDF 188KB] ( 1382 )
 479 On the Moment Convergence for Weighted Sums of Pairwise NQD Random Variables Wu Yongfeng, Shen Guangjun Under the condition of h-integrability with respect to an array of weights, the moment convergence for weighted sums of pairwise negative quadrant dependent random variables is studied. The authors obtain a new result, and solve the open problem in Sung et al. ,(2008) and improve the corresponding theorem of Cabrera and Volodin (2005). 2012 Vol. 28 (5): 479-488 [Abstract] ( 823 ) [HTML 1KB] [ PDF 183KB] ( 1650 )
 489 Kernel Estimation of the Diffusion Efficient in the Time-Dependent Diffusion Models Ma Lei, Chen Ping This paper studies non-parametric kernel estimates of the time-dependent diffusion equation based on the observations of discrete samples. We construct local kernel estimation of the time-dependent diffusion coefficient using "sectional" method. Furthermore we proved the strong consistency of the estimator. 2012 Vol. 28 (5): 489-498 [Abstract] ( 1031 ) [HTML 1KB] [ PDF 224KB] ( 1369 )
 499 Time-Varying Long Memory Parameter Estimation Based on Wavelets Lu Zhiping, Tao Qinying Stationary long memory process has been widely studied in the literature. In this article, we considered the locally stationary long memory process with time-varying memory parameter. A new wavelet-based algorithm was developed using log-linear relationship between the wavelet coefficient variance and the scaling parameter. The consistency and the finite sample behavior of the estimator have also been studied, which provide a good reference for the practitioner and researchers. The new algorithm has also been applied to the YEN/USD exchange rate series, which leads to some interesting results. 2012 Vol. 28 (5): 499-510 [Abstract] ( 976 ) [HTML 1KB] [ PDF 208KB] ( 1342 )
 511 Application in Biological Susceptibility Patterns of the Reversible Jump Markov Chain Monte Carlo Sampling Liu Ruiyin In some biological experiments, it is quite common that laboratory subjects may be different in their patterns of susceptibility to a treatment. We need to determine the different patterns of susceptibility. In this paper we model the number of susceptibility's patterns and the parameters jointly, and base inference about these quantities on their posterior probabilities, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. For convenience, we always assume different patterns of susceptibility have common variances. The paper apply the methodology to the analysis of univariate normal mixtures with different variances. The practical significance of the proposed method is illustrated with a dose-response data set. 2012 Vol. 28 (5): 511-519 [Abstract] ( 935 ) [HTML 1KB] [ PDF 277KB] ( 1333 )
 520 A Note on Random Effects Growth Curve Models Luo Youxi, Tian Maozai, Li Hanfang The robustness of regression coefficient estimator is a hot topic in regression analysis all the while. Since the response observations are not independent, it is extraordinarily difficult to study this problem for random effects growth curve models, especially when the design matrix is non-full of rank. The paper not only gives the necessary and sufficient conditions under which the generalized least square estimate is identical to the the best linear unbiased estimate when error covariance matrix is an arbitrary positive definite matrix, but also obtains a concise condition under which the generalized least square estimate is identical to the maximum likelihood estimate when the design matrix is full or non-full of rank respectively. In addition, by using of the obtained results, we get some corollaries for the the generalized least square estimate be equal to the maximum likelihood estimate under several common error covariance matrix assumptions. Illustrative examples for the case that the design matrix is full or non-full of rank are also given. 2012 Vol. 28 (5): 520-534 [Abstract] ( 1023 ) [HTML 1KB] [ PDF 213KB] ( 1541 )
 535 The Risk Model with Interest, Liquid Reserves and a Constant Dividend Barrier Wei Jiaqin, Qiu Chunjuan In this paper, we consider the compound Poisson surplus model with interest, liquid reserves and a constant dividend barrier. When the surplus of an insurer is below a fixed level, the surplus is kept as liquid reserves, which does not earn interest. When the surplus attains the level, the surplus will receive interest at a constant rate. When the surplus hits another fixed higher lever, the excess of the surplus over this higher level will be distributed to the shareholders as dividends. We derive a system of integro-differential equations for the Gerber-Shiu discounted penalty function and obtain the solutions to these integro-differential equations. In the case where the claim sizes are exponential distributed, we get the exact solutions of zero discounted Gerber-Shiu function. We also get the integro-differential equation for the expectation of the discounted dividends until ruin which is the key to discuss the optimal dividend barrier. And we give the exact solution in the special case with exponential claim sizes. 2012 Vol. 28 (5): 535-550 [Abstract] ( 1016 ) [HTML 1KB] [ PDF 219KB] ( 1425 )
 551 Bayesian Inference of Hierarchical Regression Model for zero-Inflated Clustered Count Data Shi Hongxing Zero-inflated Poisson (ZIP) regression model is a popular tool for analyzing count data with excess zeros. In this paper, a flexible hierarchical ZIP regression model is proposed to handle with such data with cluster and Bayesian approach is develop. A Gibbs sampler is employed to produce the Bayesian estimate, a goodness-of-fit and a Bayesian information criterion (BIC) are used for model comparison and selection. Finally, an application of data from a ship damage incident study illustrates the proposed method. 2012 Vol. 28 (5): 551-560 [Abstract] ( 982 ) [HTML 1KB] [ PDF 228KB] ( 1566 )

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