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2007 Vol.23 Issue.4,Published 2007-11-15

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

Wang Kaiyong, Wang Yuebao

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.
2007 Vol. 23 (4): 337-344 [Abstract] ( 2343 ) [HTML 0KB] [ PDF 515KB] ( 1674 )
345 Pricing Mortgage Insurance with House Price Driven by Poisson Jump Diffusion Process
Chen Liping, Yang Xiangqun
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.
2007 Vol. 23 (4): 345-351 [Abstract] ( 1881 ) [HTML 0KB] [ PDF 598KB] ( 1345 )
352 On the Limit Behaviour of the Population-Size-Dependent Bisexual Branching Processes
MA Shixia, WANG Yongjing
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.
2007 Vol. 23 (4): 352-360 [Abstract] ( 1833 ) [HTML 0KB] [ PDF 252KB] ( 1373 )
361 Bayesian Estimates of Distribution for Count Data with Overdispersion
CHEN Xuedong
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.
2007 Vol. 23 (4): 361-368 [Abstract] ( 1886 ) [HTML 0KB] [ PDF 592KB] ( 1296 )
369 Asymptotic Properties of Estimators in Semiparametric Regression Model for Longitudinal Data

TIAN Ping, XUE Liugen

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.
2007 Vol. 23 (4): 369-376 [Abstract] ( 2937 ) [HTML 0KB] [ PDF 530KB] ( 1602 )
377 Ergodicity of a Class of Single Death Processes
ZHANG Lihua, Zhang Yuhui
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.

2007 Vol. 23 (4): 377-383 [Abstract] ( 2084 ) [HTML 0KB] [ PDF 554KB] ( 1430 )
384 The Average Run Lengths of Control Charts for Stable L\'{e}vy Processes
Zhang Chen, HAN Dongong, TSUNG Fugee
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.
2007 Vol. 23 (4): 384-394 [Abstract] ( 2370 ) [HTML 0KB] [ PDF 298KB] ( 1557 )
395 The Martingale Approach for Credit-Risky Option Pricing
DING Deng, CHAN Kaleong
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).
2007 Vol. 23 (4): 395-406 [Abstract] ( 2110 ) [HTML 0KB] [ PDF 295KB] ( 1391 )
407 Bayesian Clustering for Ordinal Data Based on Finite Mixture Models of Latent Variables
XU Qinfeng, YU Yan, SUN Pengfei
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.
2007 Vol. 23 (4): 407-418 [Abstract] ( 2511 ) [HTML 0KB] [ PDF 1247KB] ( 1278 )
419 Monotone Empirical Bayes Test for Scale Parameter under Random Censorship
WANG Lichun
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.
2007 Vol. 23 (4): 419-427 [Abstract] ( 1950 ) [HTML 0KB] [ PDF 262KB] ( 1413 )
428 Markov-Modulated Geometric Brownian Motion and Bollinger Bands
HUNAG Xudong, Liu Wei
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.
2007 Vol. 23 (4): 428-433 [Abstract] ( 2201 ) [HTML 0KB] [ PDF 258KB] ( 1641 )
综合报告
434 Stable Distribution and its Application in Finance
WU DOng, Tang Yincai
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.
2007 Vol. 23 (4): 434-445 [Abstract] ( 1869 ) [HTML 0KB] [ PDF 1111KB] ( 1347 )
学术活动报道
446
2007 Vol. 23 (4): 446-447 [Abstract] ( 1572 ) [HTML 0KB] [ PDF 299KB] ( 1376 )
应用概率统计
 

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