Modelling the CPI using a lognormal diffusion process and implications on forecasting inflation

The Maximum Likelihood estimator is used within a lognormaldiffusion process and closed form analytical solutions are obtained.The monthly CPI forecasts are estimated for the period between1970 and 2002. The quarterly estimates of inflation rates areobtained from monthly forecasts rather than from quarterly data.This has significantly improved the estimates of inflation rates.The model also produced a superior fit as compared to randomwalk and GARCH(p,q)-M models. The adopted approach is foundto be simple, economical and generally suitable for modellingstochastic processes that reflect aggregation over time stemmingfrom many factors, and in which the transition path betweenconsecutive states is relatively smooth.     

On homeomorphisms with the two-sided limit shadowing property

We prove that the two-sided limit shadowing property is among the strongest known notions of pseudo-orbit tracing. It implies shadowing, average shadowing, asymptotic average shadowing and specification properties. We also introduce a weaker notion that is called two-sided limit shadowing with a gap and prove that it implies shadowing and transitivity. We show that those two properties allow to characterize topological transitivity and mixing in a class of expansive homeomorphisms and hence they characterize transitive (mixing) shifts of finite type.     

跳-扩散模型下的再装期权定价

本文建立股票价格的跳过程为Poisson过程,跳跃高度服从对数正态分布时股票价格过程的随机微分方程,在风险中性的假设下找到等价鞅测度,利用鞅方法,用较简单的数学推导得到了股票价格服从跳-扩散过程的欧式再装期权定价公式.     

SAMPLING INSPECTION OF RELIABILITY IN （LOG）NORMAL CASE WITH TYPE I CENSORING

This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible.     

幂型支付的欧式期权定价公式

在等价鞅测度框架下,讨论了(在到期时刻)期权处于实值状态时支付函数为幂型的股票欧式期权定价公式.这里我们假设无风险利率,股票预期收益率和股价波动率都是时间的确定性函数.本文结果不但包含了原始的Black-Scholes公式,而且可用于上封顶与下保底(幂型)欧式看涨期权的定价.     

平均跟踪与伪轨跟踪

证明了紧致度量空间中有伪轨跟踪的distal同胚不具有平均跟踪性,并给出了有平均跟踪性的同胚是极小的一个充分条件。     

Application of gradient descent method to the sedimentary grain-size distribution fitting

Existence of a least squares solution for a sum of several weighted normal functions is proved. The gradient descent (GD) method is used to fit the measured data (i.e. the laser grain-size distribution of the sediments) with a sum of three weighted lognormal functions. The numerical results indicate that the GD method is not only easy to operate but also could effectively optimize the parameters of the fitting function with the error decreasing steadily. Meanwhile the overall fitting results are satisfactory. As a new way of data fitting, the GD method could also be used to solve other optimization problems.     

对数正态分布基于恒加试验的参数估计

讨论对数正态分布场合有非常数尺度参数恒加试验的参数估计,由最小均方误差准则导出基于完全样本恒加试验的点估计和近似区间估计.