基于非仿射随机波动率模型的期权定价研究

本文应用快速傅里叶变换(FFT)方法, 考虑了标的资产服从非仿射随机波动率模型下的期权定价问题。首先, 应用偏微分方程扰动分析法, 得到了标的资产对数价格分布的近似特征函数; 然后, 应用傅里叶变换及其逆变换, 推导了欧式期权的拟闭型定价公式, 对此公式应用FFT方法可以快速得到高精度数值解。数值实验表明, FFT期权定价方法是非常精确的和有效的; 最后, 给出了基于恒生指数认购权证的实证研究。实证结果表明, 非仿射随机波动率期权定价模型比经典的Black-Scholes模型具有更高的定价精确性。     

Sensitivity measures of influence on the loading matrix in exploratory factor analysis

For the detection of influential observations on the loading matrix of the factor analysis model, we propose to use the infinitesimal version of two matrix coefficients, including Escoufier (1973)'s also discussed the application in factor analysis of some sensitivity measures used for similar purposes in principal component analysis.     

GM模型的病态性问题

本文指出GM模型的方程组存在着严重的方程病态性问题,探讨了GM模型产生病态的原因:(1)矩阵由累加数构成,累加数之间有较大的数量级差别;(2)GM模型中的蜕化使矩阵中元素数量级差别过大;(3)GM模型的矩阵生成方式使得我们难以降低方程组的病态性。并对一个被广泛引用的算例进行了分析。最后,我们认为必须小心使用GM模型。     

一类迭代泛函微分方程解的存在唯一性

利用Banach不动点定理讨论了带小扰动的一类速代泛函微分方程解的存在性和唯一性.     

Error bounds for the perturbation solution of the transition density under a multi-factor CIR term structure model with weak mean-reversion effect

Abstract

We consider a multi-factor Cox-Ingersoll-Ross (CIR) model of the term structure of interest rates with weak mean-reversion effect. We use perturbation theory to analyze its conditional characteristic function illustrated by a system of Riccati equations and derive the error bounds for the perturbation approximations. Using the Fourier inversion theorem, we clarify that the perturbation approximation of the conditional characteristic function can be applied to estimate the transition density and likelihood function. We provide their error bounds and accuracy orders. Finally, we discuss the performance of the perturbation approximation in estimating the transition density via simulation.     

Adaptive-Cox model averaging for right-censored data

In medical studies, Cox proportional hazards model is a commonly used method to deal with the right-censored survival data accompanied by many explanatory covariates. In practice, the Akaike's information criterion (AIC) or the Bayesian information criterion (BIC) is usually used to select an appropriate subset of covariates. It is well known that neither the AIC criterion nor the BIC criterion dominates for all situations. In this paper, we propose an adaptive-Cox model averaging procedure to get a more robust hazard estimator. First, by applying AIC and BIC criteria to perturbed datasets, we obtain two model averaging (MA) estimated survival curves, called AIC-MA and BIC-MA. Then, based on Kullback–Leibler loss, a better estimate of survival curve between AIC-MA and BIC-MA is chosen, which results in an adaptive-Cox estimate of survival curve. Simulation results show the superiority of our approach and an application of the proposed method is also presented by analyzing the German Breast Cancer Study dataset.     

Buck变换器在酒泉太阳能光伏发电中的应用

太阳能光伏发电作为一种新能源,易受季节变化、昼夜交替的影响,因此其输出电压很不稳定.鉴于此,本文采用Buck变换器,采用扰动观察法的MPPT控制策略,可应用到酒泉的太阳能光伏发电中,可使得输出电路的等效阻抗跟随光伏电池的输出阻抗,使光伏阵列在任何条件下获得最大功率输出,跟踪最大功率的优点.仿真表明,MPPT(最大功率跟踪)控制策略的可行性,该方法有效地提高了输出电压的稳定性.     

任意角向模数的介质切伦可夫脉塞

利用自洽线性场理论普遍讨论了相对论电子注中电子在扰动电磁场作用下的三维扰动，在此基础上，对常用的簿环形相对论电子注在介质筒慢波波导中激励的具有任意角向模数的切伦可夫辐射进行了详细的分析，导出了此电子注与慢波系统中具有任意角向模数的波导模工作用的普遍色散方程和波增长率。     

蒸发热的微扰展开

本文把液体系统中的排斥势作为相互作用势的主要部分，吸收势作为微扰，由微扰方法导出计算潜热的有关公式，给出分子相互作用势，就可由这些公式求得潜热与温度的关系，为工程上的计算提供了理论依据。