Computing the Gerber–Shiu function by frame duality projection

Inspired by some works of Kirkby, J. L. [2015. Efficient option pricing by frame duality with the fast Fourier transform. SIAM Journal on Financial Mathematics 6(1), 713–747; 2016. An efficient transform method for Asian option pricing. SIAM Journal on Financial Mathematics 7(1), 845–892], we present a systematic study on effectively computing the Gerber–Shiu function in the Lévy risk model, where the frame duality projection is used for approximation. By introducing an auxiliary function, we provide a smooth extension of the Gerber–Shiu function, which has closed-form Fourier transform and is differentiable over the whole real line under some conditions. The objective function is approximated by its frame duality projection onto a Riesz basis, and the projection coefficients are readily computed by the fast Fourier transform algorithm. Error analysis is made and the effectiveness of our results will be further illustrated in the numerical experiments.     

Testing for infinite order stochastic dominance with applications to finance, risk and income inequality

In this paper we develop a test of infinite order degree stochastic dominance based on the use of the empirical Laplace transform function. Two applications are considered. One uses the income data of Anderson (Econometrica 64:1183–1193, 1996) and derives results consistent with his. In the other application we examine the dominance between the U.S. and U.K. stock markets. Using data on the S&P 500 and the FTALL-Share we show that the U.S. displays infinite order degree stochastic dominance of the U.K.

Tail mutual exclusivity and Tail-VaR lower bounds

In this paper, we extend the concept of mutual exclusivity proposed by [Dhaene, J. & Denuit, M. (1999). The safest dependence structure among risks. Insurance: Mathematics and Economics 25, 11–21] to its tail counterpart and baptize this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency structure, at most one exceedance over the corresponding Value-at-Risks (VaRs) is possible, the other components being zero in such a case. No condition is imposed when all components stay below the VaRs. Several properties of this new negative dependence concept are derived. We show that this dependence structure gives rise to the smallest value of Tail-VaR (TVaR) of a sum of risks within a given Fréchet space, provided that the probability level of the TVaR is close enough to one.     

Estimating the Gerber–Shiu function by Fourier–Sinc series expansion

In this paper, we consider the nonparametric estimation of the Gerber–Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient estimator based on Fourier–Sinc series expansion. Our estimator is easily computed and has a faster convergence rate. Some simulation examples are provided to show that the estimator performs well when the sample size is finite.     

基于迭代FFT算法的平面稀疏阵列优化方法

提出了一种基于迭代FFT算法的优化方法来实现平面稀疏阵列的峰值旁瓣电平优化 ,并给出了详细的优化步骤。在给定的旁瓣约束条件下,利用阵列因子与阵元激励之间存在 的傅里叶变换关系,对不同的初始随机阵元激励分别进行迭代循环,就可以降低稀疏阵列的 旁瓣电平。在迭代过程中,根据稀疏率将阵元激励按幅度大小置1置0来完成阵列稀疏。仿真 实验证明了该方法的高效性和稳健性。     

一种低信噪比突发信号载波跟踪技术研究

为了改善低信噪比卫星下行短突发扩频信号载波跟踪时,解调性能随着信号动态增大而明显恶化的现象,提出了一种多普勒动态补偿辅助的载波跟踪算法,首先通过短时傅里叶变换(STFT)结合最小二乘拟合(LSM)算法估计信号频率及变化率,再利用估计值对原始信号进行多普勒动态补偿,最后使用三阶锁相环完成载波精确跟踪,对算法进行优化设计并进行仿真,以提高数据利用率。仿真结果表明,在接收-170 dBW灵敏度电平条件下,优化后的算法在对捕获后频偏小于200 Hz,频率变化率小于2 kHz/s的信号进行跟踪时,跟踪成功率达到99%,解调损失小于0.2 dB。新算法复杂度适中,利于工程实现,为现有接收机载波跟踪模块对低信噪比突发扩频信号进行改进提供了参考。     

安徽矿业经济面临六个战略转变

本文在分析现状的基础上,提出了安徽矿业经济面临的六个战略性转变,即能源开发重点应由煤逐步向煤、气、电转变;矿产资源勘查开发重点应由金属矿产向非金属矿产转变;矿业经营应由粗放型向集约型经营转变;矿业经济应由原料型向产品型转变;矿产资源勘查投资体制向多元化转变;以矿业为主导产业的城市向多元化产业城市转变.     

利用分数阶Fourier变换抑制高频地波雷达中线性调频干扰

高频地波雷达(HFGWR)受到严重的射频干扰影响。单频射频干扰在接收信号中体现为高强度的线性调频信号,从而污染所有距离元。为抑制射频干扰,通过分析其频率特征,使用分数阶傅里叶变换（FRFT）将原始信号转换到分数阶傅里叶域,对射频干扰对应的谱峰置零,达到抑制干扰的目的。该方法的优点在于抑制射频干扰的同时无损干扰位置处的回波信号,无需重构信号。实测数据分析表明：FRFT不仅能有效抑制射频干扰,信噪比提高可达10 dB以上,而且其计算复杂度较小,满足雷达实时工作要求。     

采用Gabor-Hough变换的自适应滤波人眼定位

人眼定位是人脸识别方法的第一步。传统人眼定位方法需要将人脸裁切,情况单一,对于复杂背景、倾斜等情况,精度低,宽容度差。指出将改进的滤波器与改进的定位方法相结合,首先对原图像进行Gabor变换,寻找图像凹陷,凹陷区域通过边缘像素向量改进的Hough变换检测瞳孔,得到参考坐标,经过训练得到滤波器并在角度\[-0.1,0,0.1\]旋转两次得到3个相关滤波器,通过相关滤波器滤出3个目标,选择最小误差位置作为最终的目标。相比传统方法,改进方法避免了矩阵盲目计算,具备传统方法的普适性,学习过程使定位误差减小为0.040 4,计算量减少为传统方法的1/5。该方法对不同光照、光照不均、不同表情、复杂背景、头部倾斜等情况有较好的鲁棒性,避免了单一方法定位不到和不准的情况。     

经济转型期我国区域分工演化分析

本文在探讨区域分工理论的基础上,分析了经济转型时期我国区域分工的特征与发展势态。作者指出,在全国产业结构趋同客观存在的同时,资源型区域产业虚髙度化明显,区域分工向不利于其长期战略的方向发展,进而提出了协调我国区域分工的几点设想。