一类随机利率下的增额寿险模型

对寿险中的利率随机性问题的研究是近几年来保险精算研究的热点和重点问题之一。本文以即时给付的一类增额寿险为对象,考虑到突发事件对利率的影响,对随机利率采用Gauss过程与Poisson过程联合建模,给出即时给付的增额寿险的给付现值的各阶矩,并在一些特殊条件下给出矩的简洁表达式。     

一类随机利率下的增额寿险

寿险中的利率随机问题，是近来保险精算研究的热点和重点问题之一。本以即时给付的一类增额寿险为对象，对随机利率采用Gauss过程建模，研究给付现值及其各阶矩。     

随机利率下的增额寿险

寿险中的利率随机性问题，是近年来保险精算研完的热点之一，本文以即时给付的毒额寿险为对象，对随机利率采用Gauss过程建模，研究给付现值及其各阶矩，并在死亡均匀分布假设下得到矩的简洁表达式。     

随机利率下的增额寿险模型

以即时给付的增额寿险为研究对象,在保证利率恒正的情况下,考虑到不同性质的信息对利率的影响,对利率的随机性采用带Poisson跳的反射Brown运动建模,给出了一次缴清净保费、净均衡年保费和连续缴费方式下S时刻责任准备金的一般表达式.     

随机利率寿险模型

本文针对随机利率寿险模型 ,考虑一保单组的平均给付额的性质 .通过对模型的结果分析 ,可以看出投保人数的增加 ,并未降低随机利率的风险 .本文针对一特殊的随机利率模型 ,给出了随机利率与常数利率的平均给付成本的比较     

随机利率下增额寿险现值函数矩的一些结果

本文对随机利率采用 Wiener过程和 Orentein- Uhlenbeck过程建模 ,得到了增额寿险现值函数的矩的一些结果     

一类随机利率下的变额寿险模型研究

本文对随机利率采用在原点反射的布朗运动以及负二项分布建模，具体以即时给付的综合人寿保险模型为研究对象，对寿险理论中的保费，年金以及责任准备金进行研究，并给出相应的表达式。     

变额年金与变额寿险给付额的计算

目前在人寿保险中，如何对付通货膨胀的不良影响，使对被保人的实际保障不致降低是一个重要问题。变额年金与变额寿险是因应通货膨胀的寿险产品中最有效的，但其给付额的计算比较复杂。本文扰某些变额年金与交额寿险保单的给付额的确定做了推导，并分析了利差在克服通货膨胀影响中的作用。     

随机利率下的风险模型

本文考虑一种具有随机利率的风险模型。对随机利率则取一般的独立增量过程 ,得到总索赔额精算现值的各阶矩 ,并在某些条件下给出矩的具体表达式     

息力函数综合寿险模型

本以即时给付的综合人寿保险模型为研究对象，考虑到随机利率的影响，用负二项分布和Gamma分布联合建立息力积累函数模型，求出了分期缴费精算现值和给付保险金的精算现值表达式，并可由平衡方程进行保险定价。     

Co-Recursivity and karlin-McGregor duality for indeterminate moment problems

We analyze co-recursivity for indeterminate Hamburger moment problems and the duality transformation of Karlin and McGregor for indeterminate Stieltjes moment problems. In both cases the transformed Nevanlinna matrix is given and the Nevanlinna extremal measures are discussed. An example involving associated polynomials, relevant for a quartic birth and death process, is worked out.     

Robust optimal feedback for terminal linear-quadratic control problems under disturbances

We consider a linear dynamic system in the presence of an unknown but bounded perturbation and study how to control the system in order to get into a prescribed neighborhood of a zero at a given final moment. The quality of a control is estimated by the quadratic functional. We define optimal guaranteed program controls as controls that are allowed to be corrected at one intermediate time moment. We show that an infinite dimensional problem of constructing such controls is equivalent to a special bilevel problem of mathematical programming which can be solved explicitely. An easy implementable algorithm for solving the bilevel optimization problem is derived. Based on this algorithm we propose an algorithm of constructing a guaranteed feedback control with one correction moment. We describe the rules of computing feedback which can be implemented in real time mode. The results of illustrative tests are given.     

Some Orthogonal Polynomials Related to Elliptic Functions

We characterize the orthogonal polynomials in a class of polynomials defined through their generating functions. This led to three new systems of orthogonal polynomials whose generating functions and orthogonality relations involve elliptic functions. The Hamburger moment problems associated with these polynomials are indeterminate. We give infinite families of weight functions in each case. The different polynomials treated in this work are also polynomials in a parameter and as functions of this parameter they are orthogonal with respect to unique measures, which we find explicitly. Through a quadratic transformation we find a new exactly solvable birth and death process with quartic birth and death rates.     

The Hausdorff Moment Problem under Finite Additivity

We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.     

MOMENT ESTIMATION FOR MULTIVARIATE EXTREME VALUE DISTRIBUTION

Moment estimation for multivariate extreme value distribution is described in this paper. Asymptotic covariance matrix of the estimators is given. The relative efficiencies of moment estimators as compared with the maximum likelihood and the stepwise estimators are computed. We show that when there is strong dependence between the variates, the generalized variance of moment estimators is much lower than the stepwise estimators. It becomes more obvious when the dimension increases.     

一种概率分布的极值分位数的最优估计

在本文中, 我们构造了一种新的极值分位数估计, 给出了估计量的极限性质. 同时, 在渐近二阶矩最小的准则下, 利用子样本自助法给出了计算所构造的极值分位数估计时的样本点分割方法, 从理论上证明了这一极限结果, 说明了这种分割在渐近二阶矩最小的准则下是渐近最优分割, 同时提出了自适应的样本点分割的自助算法.     

Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions

We introduce a generalized weighted digit-block-counting function on the nonnegative integers, which is a generalization of many digit-depending functions as, for example, the well known sum-of-digits function. A formula for the first moment of the sum-of-digits function has been given by Delange in 1972. In the first part of this paper we provide a compact formula for the first moment of the generalized weighted digit-block-counting function and show that a (weak) Delange type formula holds if the sequence of weights converges. The question, whether the converse is true as well, can only be answered partially at the moment. In the second part of this paper we study distribution properties of generalized weighted digit-block-counting sequences and their d-dimensional analogues. We give an if and only if condition under which such sequences are uniformly distributed modulo one.     

Plancherel–Rotach Asymptotic Expansion for Some Polynomials from Indeterminate Moment Problems

We study the Plancherel–Rotach asymptotics of four families of orthogonal polynomials: the Chen–Ismail polynomials, the Berg–Letessier–Valent polynomials, and the Conrad–Flajolet polynomials I and II. All these polynomials arise in indeterminate moment problems, and three of them are birth and death process polynomials with cubic or quartic rates. We employ a difference equation asymptotic technique due to Z. Wang and R. Wong. Our analysis leads to a conjecture about large degree behavior of polynomials orthogonal with respect to solutions of indeterminate moment problems.     

On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems

Explicit formula is given for the lifetime distribution of a consecutive-k-out-of-n:F system. It is given as a linear combination of distributions of order statistics of the lifetimes of n components. We assume that the lifetimes are independent and identically distributed. The results should make it possible to treat the parametric estimation problems based on the observations of the lifetimes of the system. In fact, we take up, as some examples, the cases where the lifetimes of the components follow the exponential, the Weibull, and the Pareto distributions, and obtain feasible estimators by moment method. In particular, it is shown that the moment estimator is quite good for the exponential case in the sense that the asymptotic efficiency is close to one.This research was partially supported by the ISM Cooperative Research Program (94-ISM-CRP-5).