Fractional normal inverse Gaussian diffusion

A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated to an inverse Gaussian process. This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times. Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a random walk with uncorrelated jumps separated by i.i.d. waiting times. The FNIG process is also derived as the limit of a fractional ARIMA processes. Finally, the NIG densities are shown to solve the relativistic diffusion equation from statistical physics.     

Marginal density estimation for linear processes with cyclical long memory

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclic effects. In particular, we extend the results of Ho and Hsing (1996), Mielniczuk (1997) and Hall and Hart (1990) to the stationary processes for which the singularities of the spectral density are not limited to the origin. We show that the convergence rates and the limiting distribution may be different in this context.     

一类推广负风险和模型的破产概率

本文研究了带干扰的两险种负风险和模型的破产问题.利用无穷小方法,给出了该风险模型破产概率所满足的微分-积分方程,并推导出破产概率满足的Lundberg型不等式.最后指出了当索赔服从负指数分布时破产概率的上界,推广了经典风险模型的结果.     

跳扩散过程下的保险商偿债率模型研究

本文研究了在有金融困境成本的情况下,带有跳扩散过程的保险商偿债率(SR)模型的问题.利用Girsanov定理进行测度变换的方法以及跳扩散过程下的看涨期权定价公式,获得了保险商终期收益的现值的结果.推广了不带跳扩散过程的保险商偿债率模型的结果.     

On the limit law of a random walk conditioned to reach a high level

We consider a random walk with a negative drift and with a jump distribution which under Cramér’s change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally positive Lévy process conditioned not to overshoot level 1.     

The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs

We extend the Rayleigh-Ritz method to the eigen-problem of periodic matrix pairs. Assuming that the deviations of the desired periodic eigenvectors from the corresponding periodic subspaces tend to zero, we show that there exist periodic Ritz values that converge to the desired periodic eigenvalues unconditionally, yet the periodic Ritz vectors may fail to converge. To overcome this potential problem, we minimize residuals formed with periodic Ritz values to produce the refined periodic Ritz vectors, which converge under the same assumption. These results generalize the corresponding well-known ones for Rayleigh-Ritz approximations and their refinement for non-periodic eigen-problems. In addition, we consider a periodic Arnoldi process which is particularly efficient when coupled with the Rayleigh-Ritz method with refinement. The numerical results illustrate that the refinement procedure produces excellent approximations to the original periodic eigenvectors.     

An effective Markov based approach for calculating the Limit Matrix in the analytic network process

Analytic network process is a multiple criteria decision analysis (MCDA) method that aids decision makers to choose among a number of possible alternatives or prioritize the criteria for making a decision in terms of importance. It handles both qualitative and quantitative criteria, that are compared in pairs, in order to forge a best compromise answer according to the different criteria and influences involved. The method has been widely applied and the literature review reveals a rising trend of ANP-related articles. The ‘power’ matrix method, a procedure necessary for the stability of the decision system, is one of the critical calculations in the mathematical part of the method. The present study proposes an alternative mathematical approach that is based on Markov chain processes and the well-known Gauss-Jordan elimination. The new approach obtains practically the same results as the power matrix method, requires slightly less time and number of calculations and handles effectively cyclic supermatrices, optimizing thus the whole procedure.     

一类非平稳高斯序列超过数点过程与和的渐近性

设{X_i}_(i=1)~∞是标准化非平稳高斯序列,N_n为X_1,X_2,…,X_n依次对水平μ_(n1),μ_(n2),…,μ_(nn)的超过数形成的点过程.记Υ_(ij)=X_iX_j,S_n=■X_i.当Υ_(ij)满足一定条件时,证明了N_n依分布收敛到Poisson过程,且N_n与S_n渐近独立.     

层次分析法在步枪作战效能评估中的应用

应用层次分析法对两代(共10种)突击步枪和自动步枪作战效能的评估和排序进行了讨论,并对其作战效能和技术水平进行了判断.所得结论对了解我军装备的先进程度,适应新时期军事科学和战备具有特别重要的意义.     

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与经典Cramer-Lundberg风险模型中保费收取过程 是时间的线性函数不同, 我们考虑聚合的保费收取过程是复合Poisson过程, 研究了在此模型下的常数分红策略问题. Dickson和Waters,(2004)指出在破产发生时, 股东还应有责任偿付破产时的赤字. 因此, 在本文中考虑的最优准则是最大化破产发生前的分红折现值与破产发生时赤字的差的期望. 做为例子, 当个体保费收取额和索赔额均为指数分布时, 给出了计算分红障碍的条件