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1.  Inventory Model with Supply Disruption Risk and Service Level Constraint  
   WANG Quan-qing  ;LI Zhen-guo  ;LI Xiao-shen《数学季刊》,2014年第3期
   We. develop a newsvender model with service level constraint for one- product, and multi-supplier system, where the supplies are susceptible to disruption risks. We prove the convexity of the programming problem,and provide the neces- sary and sufficient conditions for the optimal order quantities. Through analysis or numerical experiments we observe the effects of the disrupt risk and the service level constraint on the optimal policy. We propose some managerial insights in managing the multi-source supply chain with disruption risks.    

2.  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 continuous-time risk model in which the inter-claim 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.    

3.  Hierarchical linear regression models for conditional quantiles  被引次数:1
   TIAN Maozai & CHEN Gemai School of Statistics  Renmin University of China  Beijing 100872  China and Center for Applied Statistics  Renmin University of China  Beijing 100872  China   Department of Mathematics and Statistics  University of Calgary  Canada《中国科学A辑(英文版)》,2006年第49卷第12期
   The quantile regression has several useful features and therefore is gradually developing into a comprehensive approach to the statistical analysis of linear and nonlinear response models, but it cannot deal effectively with the data with a hierarchical structure. In practice, the existence of such data hierarchies is neither accidental nor ignorable, it is a common phenomenon. To ignore this hierarchical data structure risks overlooking the importance of group effects, and may also render many of the traditional statistical analysis techniques used for studying data relationships invalid. On the other hand, the hierarchical models take a hierarchical data structure into account and have also many applications in statistics, ranging from overdispersion to constructing min-max estimators. However, the hierarchical models are virtually the mean regression, therefore, they cannot be used to characterize the entire conditional distribution of a dependent variable given high-dimensional covariates. Furthermore, the estimated coefficient vector (marginal effects) is sensitive to an outlier observation on the dependent variable. In this article, a new approach, which is based on the Gauss-Seidel iteration and taking a full advantage of the quantile regression and hierarchical models, is developed. On the theoretical front, we also consider the asymptotic properties of the new method, obtaining the simple conditions for an n1/2-convergence and an asymptotic normality. We also illustrate the use of the technique with the real educational data which is hierarchical and how the results can be explained.    

4.  STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES  
   Wang Yi Chen Zhiping Zhang Kecun Department of Scientific Computing and Applied Softwares  Faculty of Science  Xi'an Jiaotong University  Xi'an 710049  China.《高校应用数学学报(英文版)》,2006年第4期
   In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.    

5.  STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASUREgS  
   Wang Yi Chen Zhiping Zhang Kecun《高校应用数学学报(英文版)》,2006年第21卷第4期
   In order to study the effect of different risk measures on the efficient portfolios (fron- tier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.    

6.  本刊英文版2014年57卷第10期摘要  
   《中国科学:数学》,2014年第10期
   We derive higher-order expansions of L-statistics of independent risks X1, …., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios of two kinds of risk measures, stop-loss premium and excess return on capital, respectively. Several examples and a Monte Carlo simulation study show the efficiency of our novel asymptotic expansions.    

7.  Ergodicity of a class of nonlinear time series models in random environment domain  
   En-wen Zhu  Han-jun Zhang  Gang Yang  Zai-ming Liu  Jie-zhong Zou  Shao-shun Long《应用数学学报(英文版)》,2010年第26卷第1期
   In this paper, we study the problem of a variety of p, onlinear time series model Xn+ 1= TZn+1(X(n), … ,X(n - Zn+l), en+1(Zn+1)) in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {en(i)} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented.    

8.  How does innovation's tail risk determine marginal tail risk of a stationary financial time series?  被引次数:5
   YU Bosco W. T.  PANG W. K.《中国科学A辑(英文版)》,2004年第47卷第3期
   We discuss the relationship between the marginal tail risk probability and theinnovation's tail risk probability for some stationary financial time series models. We firstgive the main results on the tail behavior of a class of infinite weighted sums of randomvariables with heavy-tailed probabilities. And then, the main results are applied to threeimportant types of time series models; infinite order moving averages, the simple bilineartime series and the solutions of stochastic difference equations. The explicit formulasare given to describe how the marginal tail probabilities come from the innovation's tailprobabilities for these time series. Our results can be applied to the tail estimation of timeseries and are useful for risk analysis in finance.    

9.  Asymptotic estimates of Gerber-Shiu functions in the renewal risk model with exponential claims  
   Li Wei《应用数学学报(英文版)》,2012年第28卷第1期
   This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.    

10.  Generalization bounds of ERM algorithm with Markov chain samples  
   Bin ZOU  Zong-ben XU  Jie XU《应用数学学报(英文版)》,2014年第30卷第1期
   One of the main goals of machine learning is to study the generalization performance of learning algorithms. The previous main results describing the generalization ability of learning algorithms are usually based on independent and identically distributed (i.i.d.) samples. However, independence is a very restrictive concept for both theory and real-world applications. In this paper we go far beyond this classical framework by establishing the bounds on the rate of relative uniform convergence for the Empirical Risk Minimization (ERM) algorithm with uniformly ergodic Markov chain samples. We not only obtain generalization bounds of ERM algorithm, but also show that the ERM algorithm with uniformly ergodic Markov chain samples is consistent. The established theory underlies application of ERM type of learning algorithms.    

11.  Epidemic propagation on adaptive coevolutionary networks with preferential local-world reconnecting strategy  
   宋玉蓉  蒋国平  巩永旺《中国物理 B》,2013年第4期
   In the propagation of an epidemic in a population, individuals adaptively adjust their behavior to avoid the risk of an epidemic. Differently from existing studies where new links are established randomly, a local link is established preferentially in this paper. We propose a new preferentially reconnecting edge strategy depending on spatial distance (PR- SD). For the PR-SD strategy, the new link is established at random with probability p and in a shortest distance with the probability 1 p. We establish the epidemic model on an adaptive network using Cellular Automata, and demonstrate the effectiveness of the proposed model by numerical simulations. The results show that the smaller the value of parameter p, the more difficult the epidemic spread is. The PR-SD strategy breaks long-range links and establishes as many short-range links as possible, which causes the network efficiency to decrease quickly and the propagation of the epidemic is restrained effectively.    

12.  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.
   

13.  The dividend function in the jump-diffusion dual model with barrier dividend strategy  
   李波  吴荣《应用数学和力学(英文版)》,2008年第29卷第9期
   A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.    

14.  Calculation and analysis of the number of return photons from sodium laser beacon excited by the long pulse laser with circular polarization  
   刘向远  ;钱仙妹  ;李玉杰  ;饶瑞中《中国物理 B》,2014年第12期
   The number of return photons from sodium laser beacon(SLB) greatly suffers down-pumping, recoil, and geomagnetic field when the long pulse laser with circular polarization interacts with sodium atoms in the mesosphere. Considering recoil and down-pumping effects on the number of return photons from SLB, the spontaneous radiation rates are obtained by numerical computations and fittings. Furthermore, combining with the geomagnetic field effects, a new expression is achieved for calculating the number of return photons. By using this expression and considering the stochastic distribution of laser intensity in the mesosphere under different turbulence models for atmosphere, the number of return photons excited by the narrow-band single mode laser and that by the narrow-band three-mode laser are respectively calculated. The results show that the narrow-band three-mode laser with a specific spectrum structure has a higher spontaneous radiation rate and more return photons than a narrow-band single mode laser. Of note, the effect of the atmospheric turbulence on the number of return photons is remarkable. Calculation results indicate that the number of return photons under the HV5/7 model for atmospheric turbulence is much higher than that under the Greenwood and Mod HV models.    

15.  A New Macro Model for Traffic Flow on a Highway with Ramps and Numerical Tests  被引次数:1
   TANG Tie-Qiao HUANG Hai-Jun S.C. Wong GAO Zi-You ZHANG Ying《理论物理通讯》,2009年第51卷第1期
   In this paper, we present a new macro model for traffic flow on a highway with ramps based on the existing models. We use the new model to study the effects of on-off-ramp on the main road traffic during the morning rush period and the evening rush period. Numerical tests show that, during the two rush periods, these effects are often different and related to the status of the main road traffic. If the main road traffic flow is uniform, then ramps always produce stop-and-go traffic when the main road density is between two critical values, and ramps have little effect on the main road traffic when the main road density is less than the smaller critical value or greater than the larger critical value. If a small perturbation appears on the main road, ramp may lead to stop-and-go traffic, or relieve or even eliminate the stop-and-go traffic, under different circumstances. These results are consistent with real traffic, which shows that the new model is reasonable.    

16.  High dimensional covariance matrix estimation using multi-factor models from incomplete information  
   XU FangFang  HUANG JianChao  WEN ZaiWen《中国科学 数学(英文版)》,2015年第4期
   Covariance matrix plays an important role in risk management, asset pricing, and portfolio allocation. Covariance matrix estimation becomes challenging when the dimensionality is comparable or much larger than the sample size. A widely used approach for reducing dimensionality is based on multi-factor models. Although it has been well studied and quite successful in many applications, the quality of the estimated covariance matrix is often degraded due to a nontrivial amount of missing data in the factor matrix for both technical and cost reasons. Since the factor matrix is only approximately low rank or even has full rank, existing matrix completion algorithms are not applicable. We consider a new matrix completion paradigm using the factor models directly and apply the alternating direction method of multipliers for the recovery. Numerical experiments show that the nuclear-norm matrix completion approaches are not suitable but our proposed models and algorithms are promising.    

17.  Flexible scheduling model of crude oil operations under crude supply disturbance  被引次数:2
   Ming Pan   Yu Qian and XiuXi Li《中国科学B辑(英文版)》,2009年第52卷第3期
   Today’s changeable market and resultant disturbance of crude oil supply require agile and flexible scheduling of crude oil operation. The objective of flexible scheduling is to keep stable crude oil op-eration and satisfy production demands under the circumstances of supply disturbance. In this paper, a new mixed integer non-linear programming (MINLP) formulation is set up for crude oil scheduling firstly, and then some heuristic rules worked out by some experts are proposed to linearize bilinear terms and ...    

18.  An analytical solution for the population balance equation using a moment method  
   Mingzhou Yu  Jianzhong Lin  Junji Cao  Martin Seipenbusch《中国颗粒学报》,2015年第1期
   Brownian coagulation is the most important inter-particle mechanism affecting the size distribution of aerosols.Analytical solutions to the governing population balance equation(PBE) remain a challenging issue.In this work,we develop an analytical model to solve the PBE under Brownian coagulation based on the Taylor-expansion method of moments.The proposed model has a clear advantage over conventional asymptotic models in both precision and efficiency.We first analyze the geometric standard deviation(GSD) of aerosol size distribution.The new model is then implemented to determine two analytic solutions,one with a varying GSD and the other with a constant GSD.The varying solution traces the evolution of the size distribution,whereas the constant case admits a decoupled solution for the zero and second moments.Both solutions are confirmed to have the same precision as the highly reliable numerical model,implemented by the fourth-order Runge-Kutta algorithm,and the analytic model requires significantly less computational time than the numerical approach.Our results suggest that the proposed model has great potential to replace the existing numerical model,and is thus recommended for the study of physical aerosol characteristics,especially for rapid predictions of haze formation and evolution.    

19.  MECHANICAL BEHAVIOR OF AMORPHOUSPOLYMERS IN SHEAR  
   张赟  黄筑平《应用数学和力学(英文版)》,2004年第25卷第10期
   Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “ viscous dissipation induced“ anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G‘ Sell et al. , thus the validity of the proposed model is verified.    

20.  Plaque components affect wall stress in stented human carotid artery: A numerical study  
   Zhen-Min Fan  Xiao Liu  Cheng-Fei Du  An-Qiang Sun  Nan Zhang  Zhan-Ming Fan  Yu-Bo Fan  Xiao-Yan Deng《Acta Mechanica Sinica》,2016年第32卷第6期
   Carotid artery stenting presents challenges of in-stent restenosis and late thrombosis, which are caused primarily by alterations in the mechanical environment of the artery after stent implantation. The present study con-structed patient-specific carotid arterial bifurcation models with lipid pools and calcified components based on magnetic resonance imaging. We numerically analyzed the effects of multicomponent plaques on the distributions of von Mises stresses (VMSs) in the patient-specific models after stenting. The results showed that when a stent was deployed, the large soft lipid pool in atherosclerotic plaques cushioned the host artery and reduced the stress within the arterial wall;how-ever, this resulted in a sharp increase of VMS in the fibrous cap. When compared with the lipid pool, the presence of the calcified components led to slightly increased stresses on the luminal surface. However, when a calcification was located close to the luminal surface of the host artery and the stenosis, the local VMS was elevated. Overall, compared with calcified components, large lipid pools severely dam-aged the host artery after stenting. Furthermore, damage due to the calcified component may depend on location.    

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