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.     

随机利率下的一类特殊年金

研究在随机利率相互独立条件下的某些延付年金的积累值的计算问题,目的在于研究积累值的期望和方差.研究了在随机利率相互独立条件下的期末付虹式年金,期末付平顶虹式年金,期末付倒虹式年金和期末付倒平顶虹式年金的积累值的期望和方差,并且给出了积累值的期望和方差的计算公式.     

一类随机利率下特殊年金的计算

研究在随机利率相互独立条件下年金初值的计算问题,主要是研究各类年金初值的期望和方差的计算公式.文章给出了随机利率相互独立条件下期末付平顶虹式年金,期末付虹式年金,期末付倒平顶虹式年金和期末付倒虹式年金的初值公式及其简化关系,推导出了这类年金初值的各阶矩的简化公式,进而获得了这类年金初值的期望计算公式和方差计算公式.     

模糊随机环境下的连续型变额生命年金

采用模糊随机理论,构建连续支付型变额生命年金模型.假定利率为三角模糊数,死亡率为随机变量.结合精算理论,给出了连续支付型变额生命年金精算现值的期望、方差以及分布函数和分位数的模糊表达式.最后,通过实证分析计算出一个在养老保险中常见的生命年金的相关值,验证模型的可行性.     

随机利率下年金的时间价值

本文首先在常数利率下讨论了递增年金、递减年金和固定增长年金的终值.进而在随机利率条件下研究了递增年金、递减年金和固定增长年金,得到了递增年金、递减年金和固定增长年金终值的期望与方差,推广了Zaks(2001)的结果.     

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...     

负超几何随机变量期望与方差的一种简捷计算

给出了负超几何分布的概率模型,通过将负超几何分布随机变量进行和式分解,比较简捷地计算了它的期望和方差,并指出文献[4]计算的期望和方差是错误的.     

尾年金分布的存在性和结构

本文主要是在年金分布的基础上, 推广、定义并研究了一类$r$尾年金分布的存在性和结构, 给出了这类分布的存在性条件, 证明了在一定条件下, $r$尾年金分布是年金分布与某一特殊$r$尾年金分布的混合.     

一类随机环境中多维分枝过程的极限理论

本文根据粒子的适应度定义了一类随机环境中的多维分枝过程,研究了它的母函数,给出了母函数的递推关系式.同时计算了过程的期望和方差,类似GaltonWatson过程,讨论了它的灭绝概率,构造了一个非负鞅W_n,并在子孙分布一阶矩和二阶矩有界的情况下证明了W_n依L~2收敛.     

完全区组设计下基于Aligned秩的有方向检验问题

本文基于Aligned秩给出了用于解完全区组设计有方向检验问题的, 我们称之为$C$-检验的检验方法. 本文分别对每个试验单元仅有一个观测值以及等重复观测值和不等重复观测值各种情形下的$C$检验进行了讨论, 并在原假设$H_0$成立时计算了上述各种情形下$C$检验统计量的数学期望和方差, 且证明了$C$检验统计量的渐近分布为正态分布.     

Optimal Dividend Payout under Compound Poisson Income

We consider an individual who receives income, which may be either positive or negative, and is allowed to pay out a dividend at any time as long as the accumulated income remains positive. In case the accumulated income become negative at some point in time, the individual declares bankruptcy, pays a penalty based on his accumulated income, and the process stops. Assuming that the input process is described by a compound Poisson process and that the individual's value is given by the accumulated dividends minus the penalty, both appropriately discounted, we demonstrate an optimal policy for paying dividends and provide an iterative means for estimating the corresponding value.     

Survival of systems with protection subject to two types of external attacks

We consider a large system that, due to its importance and (or) large economic value, should be protected from possible harmful attacks. The attacker executes two types of attacks modeled by the corresponding shock processes: those that target the repairable defense system and those that target the non-repairable ‘main’ system itself. The quality of the performance of the defense system, i.e., the ability to neutralize the attacks on the main system depends on its state defined by the accumulated damage. In order to obtain the survival probabilities for the main system, we develop a new class of state-dependent extreme shock models, where the accumulated damage caused by the shock process of one type affects the probability of failure from shocks of the other type.     

The modeling mechanism,extension and optimization of grey GM (1, 1) model

The modeling mechanism of GM (1, 1) model is studied by using the thought of matrix analysis in this paper, the extension form GGM (1, 1) model based on the fractional order accumulated generating is put forward and its theoretical significance is analyzed. Furthermore, the influence of multiple transformation, translation transformation for the initial value and generating series on model parameters and predictive value are researched, then the quantitative relation among them is deduced and an optimization model and corresponding algorithm in practical modeling are presented.     

基于主成分分析的投资决策

本文首先运用多元统计分析中的主成分分析法对上市公司投资价值的多项指标进行了综合聚集，其次在理想点的基础上建立了综合优化决策模型，并对通讯行业上市公司进行了投资分析，从而为管理者和决策者提供了一种科学而合理的决策依据和决策方法。     

Optimization of solutions in expert systems

The problem of construction of expert systems that are able to compute the optimal (with the greatest value) solution using the information accumulated in BK. The formalization of the problem is given and its mathematical model is constructed in the conditionally-extremal and game-theoretic form. The necessity of application of the methods of solution of partially defined problems of the Boolean programming and two-person zero-sum games with Boolean strategies is justified.Translated from Dinamicheskie Sistemy, No. 9, pp. 107–111, 1990.     

A posteriori computation of the singular vectors in a preconditioned Jacobi SVD algorithm

This paper describes a novel way to implement the Jacobi algorithmfor the singular value decomposition of full rank matrices.It is shown that the left and right singular vectors can becomputed without explicit accumulation of Jacobi rotations.Instead, the accumulated product of Jacobi rotations is computeda posteriori as the solution of a certain well-conditioned matrixequation. Theoretical analysis provides tools to estimate, checkand, if necessary, to improve the accuracy of the computed decomposition.Experimental results show that the new technique performs verywell in practice.     

On the choice of auxiliary linear operator in the optimal homotopy analysis of the Cahn-Hilliard initial value problem

Analytical solutions for the Cahn-Hilliard initial value problem are obtained through an application of the homotopy analysis method. While there exist numerical results in the literature for the Cahn-Hilliard equation, a nonlinear partial differential equation, the present results are completely analytical. In order to obtain accurate approximate analytical solutions, we consider multiple auxiliary linear operators, in order to find the best operator which permits accuracy after relatively few terms are calculated. We also select the convergence control parameter optimally, through the construction of an optimal control problem for the minimization of the accumulated L ²-norm of the residual errors. In this way, we obtain optimal homotopy analysis solutions for this complicated nonlinear initial value problem. A variety of initial conditions are selected, in order to fully demonstrate the range of solutions possible.     

A heuristic to reduce the wrapping effect in the numerical solution ofx′=f(t,x)

The problem of obtaining a realistic guaranteeda posteriori bound on the accumulated error in a computed solution to the initial value problem in ordinary differential equations is difficult, because of the wrapping effect. This difficulty can sometimes, but not always, be avoided by making use of coordinate transformations. In this paper we propose that the wrapping effect be reduced by enclosing the accumulated error in a convex polygon of a certain form, and we describe one possible way of choosing the faces of such a polygon. The method is computationally expensive, but provides, in cases where other methods are unable to do so, a bound which does not grow exponentially too fast.     

Volatility forecasting for interbank offered rate using grey extreme learning machine: The case of China

Interbank Offered rate is the only direct market rate in China’s currency market. Volatility forecasting of China Interbank Offered Rate (IBOR) has a very important theoretical and practical significance for financial asset pricing and financial risk measure or management. However, IBOR is a dynamics and non-steady time series whose developmental changes have stronger random fluctuation, so it is difficult to forecast the volatility of IBOR. This paper offers a hybrid algorithm using grey model and extreme learning machine (ELM) to forecast volatility of IBOR. The proposed algorithm is composed of three phases. In the first, grey model is used to deal with the original IBOR time series by accumulated generating operation (AGO) and weaken the stochastic volatility in original series. And then, a forecasting model is founded by using ELM to analyze the new IBOR series. Lastly, the predictive value of the original IBOR series can be obtained by inverse accumulated generating operation (IAGO). The new model is applied to forecasting Interbank Offered Rate of China. Compared with the forecasting results of BP and classical ELM, the new model is more efficient to forecasting short- and middle-term volatility of IBOR.