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利用极值理论给出了一种新的解决非寿险精算中巨额损失保费厘定问题的方法。在建模过程首先给出了极值理论的最大吸引域检验问题,然后利用不同方法讨论了最优门限值的选取问题,并在POT模型下利用广义帕累托分布对巨额损失分布进行拟合。然后在假设损失次数服从泊松分布的条件下,在复合泊松分布的框架下讨论了险位超赔再保险的纯保费计算问题。 相似文献
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依据极值理论构建基于GPD的POT模型,对我国1969年至2013年间地震直接经济损失数据进行拟合;选取恰当的阀值,并对模型形状参数及尺度参数进行估计,以此研究地震巨灾损失的尾部特征,从而合理的对地震巨灾风险进行度量,得到损失数据的高分位数;最后,探讨了POT模型在再保险的高超额层选取及定价问题中的应用. 相似文献
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三参数广义帕累托分布的似然矩估计 总被引:1,自引:0,他引:1
广义帕累托分布(GPD)在极值统计的POT模型中常常被用来逼近超过阈值u的超出量X_i-u的分布.
为解决经典估计方法存在的问题, Zhang (Zhang J, Likelihood moment estimation for the generalized Pareto distribution, Aust N Z J Stat,
2007, 49:69--77) 对两参数GPD (GP2)提出一种新的估计方法------似然矩估计(LM),
它容易计算且具有较高的渐近有效性. 本文将此方法从两参数的情形推广到三参数GPD (GP3),
结果表明尺度参数和形状参数估计的渐近性质与以上所提到的文章完全相同. 针对GP3的LM估计也具有总是存在、易于计算以及
对绝大多数的形状参数具有接近于最小的偏差和均方误差的特点. 相似文献
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Hilbert空间族中Тихонов正则化的Arcaugeli方法的渐近精确阶的估计 总被引:1,自引:0,他引:1
程晋 《高校应用数学学报(A辑)》1987,(3)
本文在Hilbert空间族(Hs),seR~1中,讨论了由正则化泛函‖Kfg~δ‖~2+a‖f‖_p~2所确定的正则化解的收敛性条件,给出了Arcangeli正则参数选取方法的渐近精确阶估计,另外还讨论了与正则化解收敛性有关的一些问题。 相似文献
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随机变量之间的关系一直是统计学研究中的重要问题之一.在面对不同的问题时,选取合适的方法去判断随机变量间的关系已成为解决实际问题的关键所在.针对这一现状,从概率论中的条件概率和条件分布出发,对随机变量的相关性理论与格兰杰的因果性理论进行了详细的讨论和分析,给出了判断随机变量由相关性(线性到非线性演化)到格兰杰因果性的方法.结果对于理解和把握随机变量的关系,给出恰当的判断,是有益的一种探索. 相似文献
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如何公平的实施高品质的数学教育?这是近年来数学教育领域比较关注的问题之一,在发展中国家中,对这个问题的讨论尤为热烈.我们国内这方面的工作似乎还不多见.本文试图介绍在第十一届国际数学教育大会(ICMEll)上的第五个大会讨论报告中,澳大利亚的阿特维(Bill At-weh),墨西哥的弗圭拉斯(Olimpia Figueras)、黎巴嫩的约德克(Murad Jurdak)和菲律宾的余(Catherine Vistro-Yu)就这一问题进行的讨论.相信讨论内容对于中国的教育工作者会有参考价值. 相似文献
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张家平 《数学的实践与认识》2010,40(3)
极值风险,即稀少或极端事件的发生给经济主体带来巨额损失的风险是风险管理的重中之重.极值理论为极端事件的统计建模和极值风险测度的计算提供了坚实的理论基础,通过介绍和比较传统极值事件的建模,然后基于点过程拓展了POT模型(POT-PP),并利用外汇市场的日数据分析了POT-PP的拟合效果. 相似文献
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In this paper we consider a real-time multiserver (such as machine controllers) and multichannel (such as regions and assembly lines) systems involving maintenance. Our objective is to fit these systems into the framework of queueing models and thus to justify the use of the powerful queueing theory analytical methods in the analysis of real-time systems. The main difficulty is that real-time systems by their very nature do not permit queues. To resolve this contradiction we use a dual approach in which we consider jobs as servers and servers as jobs. We adjust the traditional definition of availability for the real-time systems under consideration and show how to compute the system’s availability, when both service and maintenance times are exponentially distributed (birth-and-death process). At this stage we restrict ourselves to a worst case (maximum load regime), which is most typical in high-performance data acquisition and control (production and military) systems. 相似文献
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In this paper, we consider the Straight Line Type Node Configuration C (SLTNCC) in multivariate polynomial interpolation as the result of different kinds of transformations of lines (such as parallel translations, rotations). Corresponding to these transformations we define different kinds of interpolation problems for the SLTNCC. The expression of the confluent multivariate Vandermonde determinant of the coefficient matrix for each of these interpolation problems is obtained, and from this expression we conclude the related interpolation problem is unisolvent. Also, we give a kind of generalization of the SLTNCC in Section 5. As well, we obtain an expression of the interpolating polynomial for a kind of interpolation problem discussed in this paper. 相似文献
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时滞惯性流形及近似时滞惯性流形族 总被引:7,自引:0,他引:7
时滞惯性流形是对耗散系统惯性流形、近似惯性流形的最新发展,它基于对 大小涡分量间相互作用更细致的观察,即改变了惯性流形和近似惯性流形方法中大小 涡分量间相互作用为瞬时行为的隐含假定,而认为这种作用与系统的历史相关的.本 文结出了一类耗散系统时滞惯性流形的存在性证明,由于其存在性不需要“谱间隔条 件”保证,因而时滞惯性流形是广泛存在的.随后我们引出了一类离散的时滞惯性流 形,并在此基础上构造了一种近似时滞惯性流形族,分别给出了它们近似时滞惯性流 形的误差估计,结果显示这种新方法为构造稳定和高精度的算法提供了可能. 相似文献
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In this paper we provide a classification theorem and a structure theorem for exact differential graded algebras, and we use the classification theorem to show that a differential graded algebra A is semisimple (as a differential graded algebra) precisely when the graded algebra Z(A) is semisimple (as a graded algebra) and A is an exact complex. We also relate exact differential graded algebras with a graded version of Hochschild cohomology. 相似文献
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Alain Billionnet 《European Journal of Operational Research》1982,11(2):167-175
The records of a data base can be accessed from other records or from a set of data items (inverted access, primary and secondary index of IMS, search keys of CODASYL etc.) which we call selectors. The implementation of this selectors can use different techniques as hash coding, inverted lists or hierarchical index (indexed sequential, B-trees etc…) We consider here the last one and we search for a given set of selectors an optimal index structure. We show how this problem can be put as the search of an optimal rooted tree among the partial subgraphs of a given graph G (this problem is known in graph theory as Steiner problem) and we give several properties which allow the graph G to be notabily reduced. Then we present a branch and bound algorithm to solve this problem. 相似文献
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The set of polynomials that are nonnegative over a subset of the nonnegative orthant (we call them set-semidefinite) have many uses in optimization. A common example of this type set is the set of copositive matrices, where we are effectively considering nonnegativity over the entire nonnegative orthant and are restricted to homogeneous polynomials of degree two. Lasserre (SIAM J. Optim., 21(3):864–885, 2011) has previously considered a method using moments in order to provide an outer approximation to this set, for nonnegativity over a general subset of the real space. In this paper, we shall show that, in the special case of considering nonnegativity over a subset of the nonnegative orthant, we can provide a new outer approximation hierarchy. This is based on restricting moment matrices to be completely positive, and it is at least as good as Lasserre’s method. This can then be relaxed to give tractable approximations that are still at least as good as Lasserre’s method. In doing this, we also provide interesting new insights into the use of moments in constructing these approximations. 相似文献
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Summary In this paper we consider a class of regularization methods for a discretized version of an operator equation (which includes the case that the problem is ill-posed) with approximately given right-hand side. We propose an a priori- as well as an a posteriori parameter choice method which is similar to the discrepancy principle of Ivanov-Morozov. From results on fractional powers of selfadjoint operators we obtain convergence rates, which are (in many cases) the same for both parameter choices. 相似文献
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In this paper, we find that the idea of using optional two-part tariffs as a basis for tariff renegotiations in a bilaterally monopoly setting is a solution to the double marginalization problem that theoretically (1) creates a stable equilibrium, (2) at the overall efficient level, (3) without the presence of a central management. Through experimental testing, we find that the efficiency of this mechanism is significantly higher than the efficiency of simple direct negotiation, both under symmetrically and asymmetrically distributed information. 相似文献
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In this paper, we develop a deterministic inventory model with two warehouses (one is the existing storage known as own warehouse (OW) and the other is hired on rental basis known as rented warehouse (RW). The model allows different levels of item deterioration in both warehouses. The demand rate is supposed to be a linear (increasing) function of time and the replenishment rate is infinite. The stock is transferred from RW to OW in continuous release pattern and the associated transportation cost is taken into account. Shortages in OW are allowed and excess demand is backlogged. For the general model, we give the equations for the optimal policy and cost function and we discuss some special cases. A numerical example is given to illustrate the solution procedure of the model. Finally, based on this example, we conduct a sensitivity analysis of the model. 相似文献