20 November 2008, Volume 24 Issue 6
    

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    学术论文
  • Convergence Theorems of the Limit Processes of Integrated Errors of Semimartingale Sequence
    Xiao Xiaoqing,Xie Yingchao
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 561-573.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Jacod, Jakubowski and M\'emin studied the integrated error processes $Y^n(X)$ and $Z^{n,p}(X)$ which relates to the error process $^n\!X_t=X_t-X_{[nt]/n}$ for semimartingale $X$ with independent increments. And they also investigated the limit theorems for the semimartingale sequence $\{(Y(X^n),Z^p(X^n))\}_{n\ge 1}$. If denote the limit points of $\{(Y(X^n),Z^p(X^n))\}_{n\ge 1}$ by
    $(Y(X),Z^p(X))$, Jacod et al. gave the formula of $(Y(X),Z^p(X))$. In this paper, we will investigate the convergence theorems of $Y(X^n)$ and $Z^{p}(X^n)$ for semimartingale sequence $\{X^n\}_{n\ge 1}$. We study mainly the convergence in law and the stable convergence in law of $\{(X^n,Y(X^n),Z^p(X^n))\}_{n\ge 1}$.
  • An Approach for Constructing Some $2_{\rm{III}}^{m-(m-k)}$Designs with the Maximum Number of Clear Two-Factor Interactions
    Yang Guijun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 574-580.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    This paper provides an approach for constructing $2_{\text{III}}^{m-(m-k)}$ designs containing the maximum number of clear two-factor interactions. The designs obtained contain more clear two-factor interactions than those obtained Tang et al. (2002) for some $m$ and $k$. Moreover, the designs constructed are shown to have concise grid representations.
  • The Ruin Probability of Classical Risk Model and the Distribution of the Cycle Maximum of the M/G/1 Queue
    Xing Yongsheng, Ma Jianjing
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 581-584.
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    In this paper, the relationship of classical risk model and the M/G/1 is considered. Applying the ruin probability of risk model, the distribution of the cycle maximum of the M/G/1 queue is derived.
  • Ruin Probability for Correlated Risk Process that is Perturbed by Diffusion
    Gu Peipei, Wang Guojing
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 585-592.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In this paper, we introduce a correlated risk process that is perturbed by diffusion with common shock. We study how the dependence between the classes impacts on the ruin probability. We do this mainly by comparing the influences of the dependence on the sizes of the Lundberg exponents of the risk processes.
  • Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Exponential Family Nonlinear Models
    Xia Tian, Kong Fanchao
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 593-603.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    This paper proposes some regularity conditions which weaken those given by Zhu \& Wei (1997). On the basis of the proposed regularity conditions, the existence, the strong consistency and the asymptotic normality of maximum likelihood
    estimation (MLE) are proved in exponential family nonlinear models
    (EFNMs). Our results may be regarded as a further improvement of the
    work of Zhu \& Wei (1997).
  • Skew normal distribution, quadratic form, skewness, kurtosis.
    Fang Biqi
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 604-612.
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    In this paper, we derived the moments of the random vectors with the skew normal distributions and their quadratic forms in the general case. As an application, the measures of multivariate skewness and kurtosis are calculated.
  • The Martingale Pricing for Convertible Bond with Dividend-Paying under Stochastic Interest
    Zhu Dan, Yang Xiangqun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 613-620.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    The value composition of the convertible bond is discussed in a quantitative analysis. Under stochastic interest, the stock has dividend-paying, the pricing formulas of the convertible bond are obtained by means of Martingale approach
    (risk-neutral valuation).
  • Quick Algorithm for Least Absolute Deviation Estimator
    Lu Shulong, Liu Wenli
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 621-630.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Least square estimator (LSE) is disturbed easily by singular point; least absolute deviation estimator (LADE) can overcome the influence of singular point, but it is difficult in calculation. A convergent algorithm for LADE based on the stable
    pole theorem of LADE under non-degenerate model is obtained in this paper. The progress of algorithm and comparison of linear programming are derived. Further this algorithm makes LADE more effective.
  • The Expected Discounted Penalty at Ruin under a Stochastic Interest Rate
    Wang Houchun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 631-638.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In the classical risk model, the conception of the expected discounted penalty at ruin with a stochastic interest rate is introduced. The interest randomness is described by standard Wiener process and Poisson process. The renewal equation for the expected discounted penalty at ruin is derived, and the
    asymptotic formula for it is derived by virtue of this equation.
  • The Superiority of Bayes Linear Unbiased Estimation in the Growth Curve Model
    Zhou Jingwen, Wei Laisheng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 639-647.
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    Under quadratic loss function, the Bayes linear unbiased estimator (LUE) is derived for the growth curve model. The superiority of Bayes LUE over the generalized least square estimator (GLSE) is studied in terms of the mean square error matrix (MSEM) criterion. Finally, the superiority of the Bayes LUE of estimable functions for non-full rank case is considered further.
  • Valuation of Equity-Indexed Annuity under Jump Diffusion Process
    Qian Linyi, Zhu Liping, Yao Dingjun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2008, 24(6): 648-659.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    The Equity-Indexed Annuity (EIA) contract offers a proportional participation in the return on a specified equity index, in addition to a guaranteed return on the
    single premium. In general, valuation of Equity-Indexed Annuity is often assumed that the equity index is within the Black-Scholes framework. But some rare events (release of an unexpected economic figure, major political changes or even a natural disaster in a major economy) can lead to brusque variations in prices. So in the present work we study the equity index following a jump diffusion process. By Esscher transform, we obtain a closed form of the valuation of point-to-point EIA, which can be expressed as a function of some pricing factors. Finally, we conduct several numerical experiments in which, the break even participation rate $\alpha$ can be solved when the other factors are fixed. The relationship between $\alpha$ and the other factors are also discussed.
Chinese Journal of Applied Probability and Statistics (Bimonthly)
（started publication in 1985）
Superintendent: Chinese Society of Probability and Statistics
Editor-in-Chief: Chen Mufa
ISSN 1001-4268
CN 31-1256
Mailing code: 4-414
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