一类随机利率下的确定年金

我们考虑在一定的约束条件下利率是随机变量的某些确定年金的现值的计算问题,目的在于研究给付现值的期望和方差.本文给出两种方法计算在某些年内一类延付年金的现值之和的期望和方差,获得了给付现值的方差的递推关系,并且解决了这些关系,这在计算简单方面明显地更好.     

随机利息力下的一类年金的时间价值

对于年金的时间价值的研究,往往假定利率在整个期间内是固定不变的,但事实上,由于受到多种因素的影响,利率通常具有不确定性.因此,本文采用可逆MA(1)模型对随机利息力进行建模,在此基础上,研究了期末付虹式年金和期末付平顶虹式年金的时间价值问题,给出了上述两种形式年金现值的期望和方差的递推公式.通过数值仿真分析了相关参数对...     

利用随机变量的和式分解计算数字特征

通过两个典型实例展示利用随机变量的和式分解可简化其数字特征的计算过程.     

模糊随机变量的数字特征

本文给出了模糊随机变量的方差这一概念,并讨论了它的一些性质及计算方法。     

概率论与数理统计中的若干反例分析

本文指出了两篇概率论与数理统计文献中存在的错误,并通过若干例子给予说明.     

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     

一类随机利率模型下的年金精算现值

年金在日常生活中被广泛应用,但已往大多研究的是固定年金以及随机利率下的确定年金.本文在前人研究成果的基础上考虑了利率随机波动对生命年金的影响,运用随机利率模型,得出年金精算现值较为简单的递推关系式,并举例说明利率的随机波动对年金精算现值的影响程度,结果表明利率的波动对年金的定价影响非常大,绝对不容忽视.     

基于广义条件AR(p)利率下的生存年金精算现值模型及其应用

本文利用时间序列理论将投资利率为条件 AR(p)模型推广为广义条件 AR(p)模型 ,得到利息力模型的一阶矩和二阶矩 ;针对年末支付的定期生存年金 ,利用生存年金理论得到广义条件 AR(p)利率模型下生存年金的精算现值模型 ,这对保险人合理制定保费标准和规避风险等问题具有重要理论指导意义和实际应用价值 .     

基于分布函数的混合型随机变量数学期望和方差的计算

在文献[1]的基础上,利用分布函数,介绍一种适合工科概率论教学的混合型随机变量的数学期望和方差的计算方法.     

Poisson-Charlier多项式的若干性质

给出了Charlier多项式的若干性质及证明,并且讨论了当Charlier多项式中的自变量为Poisson随机变量时具有的性质.     

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     

独立阵列和的最大值完全收敛的等价条件

本文得到了独立阵列和(含加权和)的最大值完全收敛的等价条件,从而丰富和强化了前人的结果．     

UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE

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 heavy-tailed class L ∩ D and the discount factors (financial risk) {Yk,k=1,2,···} concentrate on [θ,L],where 0 θ 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: 1278–1299).     

债券价值对市场利率变化的敏感度

有关长期债券的价值对市场利率变化的敏感度高于短期债券的价值对市场利率变化的敏感度,本文给出了它成立的条件及它不成立的条件.     

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH (II)

This paper studies the value distribution of random analytic Dirichlet series f:(s) = ∞∑n=1 Zn(ω)e-sλn,where {Zn} is a sequence of independent random variables,n=1 with moments zero,such that infE{｜Zn｜}/E1/2{｜Zn｜2} σ ＞ 0.Suppose [h*(σ)]2 =∞∑n=1 E{｜Zn｜2}e-2σλn converges for any σ ＞ 0,and diverges for σ = 0.It is shown that if then with probability one,where β is a constant depending only upon the constant α.     

CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

We consider a branching random walk with a random environment in time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The environment is supposed to be independent and identically distributed. For AR, let Zn(A) be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn(·) with appropriate normalization.     

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH(I)

1IntroductionandtheMainResultTheBorelpointsofrandomanajyticDirichletserieshavebeenstudied[1'2]oilthecon(litiollthatthecoefficientsoftherandomDirichletseriesareindependentrandomvariables,sucfl;lstheRademacliersequencettheSteinhausesequence!andtheN-sequence.[1]Thepresentpaperdealswiththesimilarproblem,andintendstoobtainmoreaccurate(inasence)resultthan[2,Theorem4]evenifthecoefficientsofrandomDirichletseriesareassumedtobeamartingaledifferencesequence.ConsidertherandomDirichletseriesfi(s)=Zn=I…     

可列值随机变量序列的一个小偏差定理

本文得到了可列值随机变量序列的用不等式表示的强极限定理,即小偏差定理,包含了［１］的结果．［１］中研究的是相对于齐次Ｍａｒｋｏｖ 链的偏差,而本文允许非齐次的情形．     

EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.