15 November 2007, Volume 23 Issue 4
    

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    学术论文
  • Notes on the Asymptotics of the Tail Probabilities of Sums for Negatively Associated Random Variables with Heavy Tails

    Wang Kaiyong, Wang Yuebao

    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 337-344.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    This paper obtains some asymptotics for the tail probabilities of maximum of sums, random sums and maximum of idetically distributed, negatively associated random variables with heavy tails. The obtained results weaken the conditions of the moments of Theorem 2.1 in Wang and Tang (Statist. Prob. Lett., 68, 287--295, 2004). We also discuss the conditions of Theorem 2.2 of [1] and remove the restrictions of the supports of random variables.
  • Pricing Mortgage Insurance with House Price Driven by Poisson Jump Diffusion Process
    Chen Liping, Yang Xiangqun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 345-351.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Under the assumptions that a house price process driven by nonhomogeneous Poisson jump-diffusion process, and unpaid money driven by general diffusion process, we analyze the pricing of mortgage insurance by the method of insurance actuary pricing and the principle of option pricing, and obtain the accurate formulas of two kinds of mortgage insurance.
  • On the Limit Behaviour of the Population-Size-Dependent Bisexual Branching Processes
    MA Shixia， WANG Yongjing
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 352-360.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In this paper, a bisexual Galton-Watson branching process with the law of offspring distribution dependent on the population size is investigated. Under a suitable assumption on the offspring distribution, for the supercritical case, the limit behaviours on almost sure convergence of the process are established.
  • Bayesian Estimates of Distribution for Count Data with Overdispersion
    CHEN Xuedong
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 361-368.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    This paper deals with two classes distribution of count data with overdispersion:
    Zero-inflated Distribution and Inflated-parameter Distribution, which are accordance with data of claims. We consider several model formulations of those distributions by using Bayesian theory and MCMC methods in WinBUGS. By comparison, a approach of modelling data is obtained and two illustrations with real data are provided.
  • Asymptotic Properties of Estimators in Semiparametric Regression Model for Longitudinal Data

    TIAN Ping, XUE Liugen

    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 369-376.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In this paper, we consider the following semiparametric regression model for
    longitudinal data: $y_{ij}=x_{ij}'\beta+g(t_{ij})+e_{ij}$. The estimators of $\beta$ and $g(\cdot)$ are obtained by using the least squares and usual nonparametric weight function method, the asymptotic normality of the estimator of $\beta$ and the optimal convergence rate of the estimator of $g(\cdot)$ are proved under the suitable conditions. Some simulations are conducted to demonstrate the finite sample performances of the estimation procedures.
  • Ergodicity of a Class of Single Death Processes
    ZHANG Lihua, Zhang Yuhui
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 377-383.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In this paper, we consider the single death processes which go out of reversed Markov context. By comparing with the moments of hitting time of birth-death processes and stochastic comparability, some sufficient conditions and necessary conditions are obtained for some kinds of ergodicity of the single death processes respectively. Finally, one example are given to illustrate the results.

  • The Average Run Lengths of Control Charts for Stable L\'{e}vy Processes
    Zhang Chen, HAN Dongong, TSUNG Fugee
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 384-394.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    As we know that the average run length (ARL) is an extensively used measure in
    statistical process control (SPC) for evaluating and comparing the detection
    performance of various control charts. In this paper we not only present the
    asymptotic estimation of the ARL for the exponentially weighted moving average (EWMA), generalized EWMA (GEWMA) and generalized likelihood ratio (GLR) control charts but also compare the detection performance by the numerical simulation among the four charts: EWMA, GEWMA, GLR and CUSUM in detecting the mean change of a stable L\'{e}vy process.
  • The Martingale Approach for Credit-Risky Option Pricing
    DING Deng, CHAN Kaleong
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 395-406.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    The financial model for derivatives with counterparty risk is considered. The firm value model is applied to price European type options for derivatives with counterparty default risk. The martingale approach is used to derive an explicit pricing formula for such Black-Scholes option under the Gaussian assumptions, which generalize the results in [1] (Ammann, 2001).
  • Bayesian Clustering for Ordinal Data Based on Finite Mixture Models of Latent Variables
    XU Qinfeng, YU Yan, SUN Pengfei
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 407-418.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    Based on finite mixture models of latent variables, we propose a Bayesian clustering method for ordinal data. EM algorithm is employed to compute the estimates of model parameters, BIC criterion is adopted to determine the number of clusters, and an analogue procedure of Bayesian discrimination is used to classify each observation. The results of a simulation study show that the method works well, and the computing efficiency is acceptable for a dataset of moderate size.
  • Monotone Empirical Bayes Test for Scale Parameter under Random Censorship
    WANG Lichun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 419-427.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    We study the two-action problem in the scale-exponential family via the empirical
    Bayes (EB) approach and present a monotone EB test possessing a rate of convergence which can be arbitrarily close to $O(n^{-1})$ under the condition that the past samples are randomly censored from the right.
  • Markov-Modulated Geometric Brownian Motion and Bollinger Bands
    HUNAG Xudong, Liu Wei
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 428-433.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    In the stock market, Bollinger bands as a popular technical analysis tool are widely used by traders. There are a lot of models built to forecast the stock price, so it is a significant issue to investigate whether these models have Bollinger band property. Liu, Huang and Zheng (2006) and Liu and Zheng (2006) discussed the Bollinger bands for Black-Scholes model and stochastic volatility model as real stock markets, respectively. The stationarity and the law of large number of the corresponding statistics were proved. In this paper, we extend the above results to the general model of Markov-modulated geometric Brownian motion.
    • 综合报告
  • Stable Distribution and its Application in Finance
    WU DOng, Tang Yincai
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2007, 23(4): 434-445.
    Abstract ( ) Download PDF ( ) Knowledge map Save
    This paper introduces the some basic properties of Stable distributions. It is
    found from histograms and stablized PP plots of some stock-index return data that theirs distributions have a high-Kurtosis and fat-tail characteristic. It is shown from empirical study that stable distributions show more efficiency than others distribution for the return series. Finally, an application is carried out showing the efficiency of stable distributions in risk valuation of finance.
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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