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2008 Vol.24 Issue.6,
Published 2008-11-20
学术论文
561
Convergence Theorems of the Limit Processes of Integrated Errors of Semimartingale Sequence
Xiao Xiaoqing,Xie Yingchao
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 $\{(X^n,Y(X^n),Z^p(X^n))\}_{n\ge 1}$.
2008 Vol. 24 (6): 561-573 [
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2286
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1551
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574
An Approach for Constructing Some $2_{\rm{III}}^{m-(m-k)}$Designs with the Maximum Number of Clear Two-Factor Interactions
Yang Guijun
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.
2008 Vol. 24 (6): 574-580 [
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1847
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182KB] (
1380
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581
The Ruin Probability of Classical Risk Model and the Distribution of the Cycle Maximum of the M/G/1 Queue
Xing Yongsheng, Ma Jianjing
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.
2008 Vol. 24 (6): 581-584 [
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2032
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176KB] (
1722
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585
Ruin Probability for Correlated Risk Process that is Perturbed by Diffusion
Gu Peipei, Wang Guojing
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.
2008 Vol. 24 (6): 585-592 [
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2062
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198KB] (
1515
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593
Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Exponential Family Nonlinear Models
Xia Tian, Kong Fanchao
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).
2008 Vol. 24 (6): 593-603 [
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2386
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211KB] (
1516
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604
Skew normal distribution, quadratic form, skewness, kurtosis.
Fang Biqi
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.
2008 Vol. 24 (6): 604-612 [
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2055
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187KB] (
1526
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613
The Martingale Pricing for Convertible Bond with Dividend-Paying under Stochastic Interest
Zhu Dan, Yang Xiangqun
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).
2008 Vol. 24 (6): 613-620 [
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1896
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1630
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621
Quick Algorithm for Least Absolute Deviation Estimator
Lu Shulong, Liu Wenli
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.
2008 Vol. 24 (6): 621-630 [
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2807
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2798
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631
The Expected Discounted Penalty at Ruin under a Stochastic Interest Rate
Wang Houchun
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.
2008 Vol. 24 (6): 631-638 [
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1927
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1592
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639
The Superiority of Bayes Linear Unbiased Estimation in the Growth Curve Model
Zhou Jingwen, Wei Laisheng
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.
2008 Vol. 24 (6): 639-647 [
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1956
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206KB] (
1449
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648
Valuation of Equity-Indexed Annuity under Jump Diffusion Process
Qian Linyi, Zhu Liping, Yao Dingjun
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.
2008 Vol. 24 (6): 648-659 [
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2257
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229KB] (
1795
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应用简报
660
2008 Vol. 24 (6): 660-665 [
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1568
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231KB] (
1546
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666
2008 Vol. 24 (6): 666-670 [
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2047
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186KB] (
2763
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学术活动报道
671
2008 Vol. 24 (6): 671-672 [
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1488
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78KB] (
1495
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