1.

On tail behavior of nonlinear autoregressive functional conditional heteroscedastic model with heavytailed innovations





PAN Jiazhu & WU Guangxu LMAM and School of Mathematical Sciences Peking University Beijing 100871 China《中国科学A辑(英文版)》,2005年第48卷第9期


We study the tail probability of the stationary distribution of nonparametric non linear autoregressive functional conditional heteroscedastic (NARFCH) model with heavy tailed innovations.Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance.When the innovations are heavytailed,the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations.We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the con ditional variance function.Some examples are given.

2.

Ruin probabilities with insurance and financial risks having an FGM dependence structure





CHEN Yu YANG YingYing《中国科学 数学(英文版)》,2014年第57卷第5期


We consider a discretetime risk model,in which insurance risks and financial risks jointly follow a multivariate FarlieGumbelMorgenstern distribution,and the insurance risks are regularly varying tailed.Explicit asymptotic formulae are obtained for finitetime and infinitetime ruin probabilities.Some numerical results are also presented to illustrate the accuracy of our asymptotic formulae.

3.

Nonlinear autoregressive models with heavytailed innovation





JIN Yang & AN Hongzhi School of Statistics Renmin University of China Beijing 100872 China Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China《中国科学A辑(英文版)》,2005年第48卷第3期


In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlinear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavytailed probability property with the same index as that of the innovation's tail probability.

4.

The Finite Time Ruin Probability with the Same Heavytailed Insurance and Financial Risks 被引次数：4





YiqingChen XiangshengXie《应用数学学报(英文版)》,2005年第21卷第1期


This note complements a recent study in ruin theory with risky investment by establishing the same asymptotic estimate for the finite time ruin probability under a weaker restriction on the financial risks. In particular, our result applies to a critical case that the insurance and financial risks have Paretotype tails with the same regular index.

5.

Asymptotic Ruin Probabilities of the Renewal Model with Constant Interest Force and Dependent Heavytailed Claims





Jinzhu Li Rong Wu School of Mathematical Sciences LPMC Nankai University Tianjin China《应用数学学报(英文版)》,2011年第27卷第2期


In this paper,we investigate the asymptotic behavior for the finite and infinitetime ruin probabilities of a nonstandard renewal model in which the claims are identically distributed but not necessarily independent. Under the assumptions that the identical distribution of the claims belongs to the class of extended regular variation(ERV) and that the tails of joint distributions of every two claims are negligible compared to the tails of their margins,we obtain the precise approximations for the finite and infinitetime ruin probabilities.

6.

Extension of Some Classical Results on Ruin Probability to Delayed Renewal Model 被引次数：2





Chun Su Tao Jiang Qihe TangDepartment of Statistics and Finance University of Science and Technology of China Hefei 230026《应用数学学报(英文版)》,2002年第18卷第4期


Embrechts and Veraverbeke investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities (?)(x) under the assumption that the claim size is heavytailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model.

7.

Large deviations for generalized compound Poisson risk models and its bankruptcy moments 被引次数：7





HU YijunSchool of Mathematics and Statistics Wuhan University Wuhan 430072 China《中国科学A辑(英文版)》,2004年第47卷第2期


We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function. For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.

8.

Tail behavior of supremum of a random walk when Cramér’s condition fails





Changjun Yu Yuebao Wang《Frontiers of Mathematics in China》,2014年第9卷第2期


We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavytailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and Osubexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.

9.

The gerbershiu expected discounted penalty function for Lévy insurance risk processes





Xianghua Zhao Chuancun Yin《应用数学学报(英文版)》,2010年第26卷第4期


In this paper,we study a general Lévy risk process with positive and negative jumps.A renewal equation and an infinite series expression are obtained for the expected discounted penalty function of this risk model.We also examine some asymptotic behaviors for the ruin probability as the initial capital tends to infinity.

10.

UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE 被引次数：1





明瑞星 何晓霞 胡亦钧 刘娟《数学物理学报(B辑英文版)》,2010年第30卷第3期


We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavytailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 12781299）.

11.

Exact tail asymptotics for a discretetime preemptive priority queue





Yang SONG Zaiming LIU Hongshuai DAI《应用数学学报(英文版)》,2015年第31卷第1期


In this paper, we consider a discretetime preemptive priority queue with different service completion probabilities for two classes of customers, one with highpriority and the other with lowpriority. This model corresponds to the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server. Due to the possibility of customers’ arriving and departing at the same time in a discretetime queue, the model considered in this paper is more complicated than the continuoustime model. In this model, we focus on the characterization of the exact tail asymptotics for the joint stationary distribution of the queue length of the two types of customers, for the two boundary distributions and for the two marginal distributions, respectively. By using generating functions and the kernel method, we get the exact tail asymptotic properties along the direction of the lowpriority queue, as well as along the direction of the highpriority queue.

12.

Restricted normal mixture QMLE for nonstationary TGARCH(1, 1) models





WANG Hui PAN JiaZhu《中国科学 数学(英文版)》,2014年第57卷第7期


The threshold GARCH(TGARCH)models have been very useful for analyzing asymmetric volatilities arising from financial time series.Most research on TGARCH has been directed to the stationary case.This paper studies the estimation of nonstationary first order TGARCH models.Restricted normal mixture quasimaximum likelihood estimation(NMQMLE)for nonstationary TGARCH models is proposed in the sense that we estimate the other parameters with any fixed location parameter.We show that the proposed estimators(except location parameter)are consistent and asymptotically normal under mild regular conditions.The impact of relative leptokursis and skewness of the innovations’distribution and quasilikelihood distributions on the asymptotic efficiency has been discussed.Numerical results lend further support to our theoretical results.Finally,an illustrated real example is presented.

13.

Precise Large Deviations for a Customerbased Individual Risk Model





Xuemin Ma School of Mathematics Statistics Wuhan University Wuhan China《应用数学学报(英文版)》,2011年第27卷第2期


In this paper,we propose a customerbased individual risk model,in which potential claims by customers are described as i.i.d.heavytailed random variables,but different insurance policy holders are allowed to have different probabilities to make actual claims.Some precise large deviation results for the prospectiveloss process are derived under certain mild assumptions,with emphasis on the case of heavytailed distribution function class ERV(extended regular variation).Lundberg type limiting results on the finite time ruin probabilities are also investigated.

14.

A class of delayed renewal risk processes with a threshold dividend strategy





Wuyuan Jiang Zaiming Liu《应用数学学报(英文版)》,2010年第26卷第2期


This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the GerberShiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding CerberShiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.

15.

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims





Xie Jiehua Zou Wei Wang Dehui《数学研究通讯：英文版》,2013年第3期


In this paper, we consider a risk model in which two types of individual claims, main claims and byclaims, are defined. Every byclaim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discretetype individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.

16.

Exponential Bounds for Ruin Probability in Two Moving Average Risk Models with Constant Interest Rate





Ding Jun YAO Rong Ming WANG《数学学报(英文版)》,2008年第24卷第2期


The authors consider two discretetime insurance risk models. Two moving average risk models are introduced to model the surplus process, and the probabilities of ruin are examined in models with a constant interest force. Exponential bounds for ruin probabilities of an infinite time horizon are derived by the martingale method.

17.

A local limit theorem for the probability of ruin 被引次数：3





YIN ChuancunDepartment of Mathematics Qufu Normal University Qufu 273165 China 《中国科学A辑(英文版)》,2004年第47卷第5期


In this paper, we give a result on the local asymptotic behaviour of the probability of ruin in a continuoustime risk model in which the interclaim times have an Erlang distribution and the individual claim sizes have a distribution that belongs to S(v) with v≥ 0, but where the Lundberg exponent of the underlying risk process does not exist.

18.

On the Effects of Risk Pooling in Supply Chain Management： Review and Extensions





Xia Cai and Donglei Du《应用数学学报(英文版)》,2009年第25卷第4期


The primary challenge in supply chain management （SCM） is matching supply with uncertain demand. Risk pooling is an efficient and promising strategy to meet this challenge by reducing the underlying demand uncertainty through aggregation. The main focus of this paper is to analyze the effects of risk pooling under different supply chain settings. There are two main contributions. First, we propose a mathematical framework which serves the multipurpose of （1） unifying existing models on risk pooling in the literature, （2） providing new facets and insights of understanding existing results on risk pooling, and （3） setting up new ground for extending existing models and results. Second; we investigate one interesting effect of risk pooling, namely, the decreasing marginal return （or supermodularity）. We show that there are decreasing marginal returns in risk pooling practices under certain conditions, specifically when the demand is independent and identically distributed （I.I.D.） and normally distributed.

19.

Local asymptotic behavior of the survival probability of the equilibrium renewal model with heavy tails





JIANG Tao & CHEN Yiqing School of Finance. Nanjing University of Finance and Economics Nanjing 210003 China School of Economics and Management Guangdong University of Technology Guangzhou 510090 China《中国科学A辑(英文版)》,2005年第48卷第3期


Recently, Tang established a local asymptotic relation for the ruin probability in the CramerLundberg risk model. In this short note we extend the corresponding result to the equilibrium renewal risk model.

20.

本刊英文版2009年52卷第7期摘要





《中国科学A辑》,2009年第7期


Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations PENG ShiGe Abstract This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Ito＇s type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems.
