常利率下的Cox模型的破产概率

讨论了常利率下的Cox模型的破产概率 ,分别得到了条件破产概率和最终破产概率所满足的积分方程 .     

常利率下带干扰的Cox模型的破产概率

讨论了常利率下带干扰的Cox模型的破产概率,分别得到了条件破产概率和最终破产概率所满足的微积分方程.     

竞争型的n元风险模型

保险市场中存在激烈的竞争,针对这种情形提出竞争型的n元风险模型,定义了两种破产时间,利用经典风险模型已有结论和条件期望的性质,得到相应的有限时间破产概率和最终破产概率表达式,以及每个保险公司有限时间破产概率和最终破产概率.     

马氏利率下相关险种的离散风险建模和破产概率

在随机利率服从有限齐次Markov链下,建立相关险种离散风险模型,采用递推方法得到了有限时间破产概率的递推等式和最终破产概率的积分等式;给出了有限时间破产概率和最终破产概率的上界,导出了破产时刻余额分布的计算等式.     

变破产下限风险模型的破产概率

近年来,很多文献对经典风险模型作了研究,并得出许多有用的结论。一般文献都是假定保险公司的破产下限为零,但在实际的保险实务中,当保险公司的盈余低于某一限度时,保险公司就要调整政策或宣布破产。本文研究了经典风险模型在假定变破产下限下的破产概率,得出了破产概率所满足的不等式,而且研究了当破产下限f(t)为某些特殊函数时,破产概率所满足的不等式或破产概率的具体表达式。最后本文给出了在推广后的风险模型中变破产下限破产概率所满足的不等式。     

索赔额是指数分布的马氏风险模型的破产概率

本文研究了马氏风险模型的破产概率,在索赔额服从指数分布或混合指数分布情形,通过解破产概率所满足的微积方程组,给出了破产概率的解析表达式.     

稀疏过程下变破产下限多元相依风险模型的破产概率

研究了稀疏过程下多元相依风险模型在假定变破产下限的破产概率,其中索赔产生时依赖概率ρ的可能性同时产生一次续保,即续保过程是索赔的ρ-稀疏过程.运用鞅方法得到了当破产下限为某些特征函数时破产概率所满足的不等式或破产概率的具体表达式.     

带息双二项风险模型的破产问题

本文研究了带随机利率的双二项风险模型的破产问题,得到了描述破产严重程度的破产前盈余分布,破产持续时间分布的递推公式,有限时间破产概率的递推公式及终极破产概率满足的积分方程.     

寿险中的破产理论及应用

本文研究了求解寿险中破产概率的简洁方法 ,得到寿险破产模型 ,设计了求解寿险中的破产概率的一种算法 ,并得到寿险破产概率的一个上界。     

竞争型二元风险模型破产概率

本文研究了竞争型的二元风险模型,定义了两类破产概率以及状态过程,利用经典风险模型的已有结果和条件期望的性质,得到两类破产概率表达式,以及单个保险公司有限时间破产概率和最终破产概率,并给出两个保险公司的状态过程的概率分布列.     

二次曲面和平面位置关系的判式

在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离.     

A Barrier Function Method for the Nonconvex Quadratic Programming Problem with Box Constraints

In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace.     

Staircase Parameterization in Dynamical Selection

This paper deals with a variant of a dynamical selection scheme introduced by Attouch and Cominetti for ill-posed convex minimization which combines approximation with the steepest descent method by mean of a suitable parameterization of the approximation parameter as a function of the time. This variant applies to a general inclusion with a maximal monotone operator by mean of a staircase parameterization. A discrete analogue is also considered. Applications to selecting a particular zero of a maximal monotone operator or a particular fixed point of a nonexpansive mapping via regularization techniques are presented. Finally, the alternative use of well-posedness by perturbations is discussed.     

New parameters of subsets in polynomial association schemes

We define new parameters, a zero interval and a dual zero interval, of subsets in P- or Q-polynomial association schemes. A zero interval of a subset in a P-polynomial association scheme is a successive interval index for which the inner distribution vanishes, and a dual zero interval of a subset in a Q-polynomial association scheme is a successive interval index for which the dual inner distribution vanishes. We derive bounds of the lengths of a zero interval and a dual zero interval using the degree and dual degree respectively, and show that a subset in a P-polynomial association scheme (resp. a Q-polynomial association scheme) having a large length of a zero interval (resp. a dual zero interval) induces a completely regular code (resp. a Q-polynomial association scheme). Moreover, we consider the spherical analogue of a dual zero interval.     

On fractional powers of a pair of matrices and a plate-beam problem

In this paper we consider the transversal deflections of a dynamically-coupled Von Kármán system consisting of a plate which has a beam attached to its one edge. The problem is considered in the form of a non-linear evolution problem in a product space. We show the existence of a unique local solution by following a fractional powers approach to first construct a “weak” solution in a larger space. Regularity properties for this solution yield a unique local strong solution for the original boundary-value problem. This approach entails the introduction of fractional powers of a pair of matrices.     

A conjecture on bipartite graphical regular representations

In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR.First, we find a natural obstruction that prevents a finite group from admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR.Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR.     

Scalarization of Henig Proper Efficient Points in a Normed Space

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.     

Diagrams of divide links

Recently N. A'Campo suggested a construction of a link from a generic immersion of a curve into a 2-disk. It is tightly related to the singularity theory. In this paper, we give a simple procedure to draw a diagram of the link from a picture of the curve.

     

On arithmetic Macaulayfication of Noetherian rings

The Rees algebra is the homogeneous coordinate ring of a blowing-up. The present paper gives a necessary and sufficient condition for a Noetherian local ring to have a Cohen-Macaulay Rees algebra: A Noetherian local ring has a Cohen-Macaulay Rees algebra if and only if it is unmixed and all the formal fibers of it are Cohen-Macaulay. As a consequence of it, we characterize a homomorphic image of a Cohen-Macaulay local ring. For non-local rings, this paper gives only a sufficient condition. By using it, however, we obtain the affirmative answer to Sharp's conjecture. That is, a Noetherian ring having a dualizing complex is a homomorphic image of a finite-dimensional Gorenstein ring.

     

Some iterative methods for finding fixed points and for solving constrained convex minimization problems

The present paper is divided into two parts. In the first part, we introduce implicit and explicit iterative schemes for finding the fixed point of a nonexpansive mapping defined on the closed convex subset of a real Hilbert space. We establish results on the strong convergence of the sequences generated by the proposed schemes to a fixed point of a nonexpansive mapping. Such a fixed point is also a solution of a variational inequality defined on the set of fixed points. In the second part, we propose implicit and explicit iterative schemes for finding the approximate minimizer of a constrained convex minimization problem and prove that the sequences generated by our schemes converge strongly to a solution of the constrained convex minimization problem. Such a solution is also a solution of a variational inequality defined over the set of fixed points of a nonexpansive mapping. The results of this paper extend and improve several results presented in the literature in the recent past.