A regression-based smoothing spline Monte Carlo algorithm for pricing American options in discrete time

American options in discrete time can be priced by solving optimal stopping problems. This can be done by computing so-called continuation values, which we represent as regression functions defined recursively by using the continuation values of the next time step. We use Monte Carlo to generate data, and then we apply smoothing spline regression estimates to estimate the continuation values from these data. All parameters of the estimate are chosen data dependent. We present results concerning consistency and the estimates’ rate of convergence.     

发展战略与经济收敛：以中国各省份为样本

 目前一些学者对于发展战略与经济收敛的研究结论存在较大分歧。本文提出了一个基于动态比较优势的发展战略与地区经济收敛的分析框架,给出了一个较为全面的新解释。本文的主要论点是：落后地区代表性生产部门加大物质资本与人力资本投入,引进或研发较为先进的生产技术,加快工业化进程,实行赶超战略有利于缩小本地区与领先地区间的经济差距增长的速度,甚至于实现经济收敛。并以我国改革开放以来各省区的经济增长现实验证了理论假说的合理性。     

初等概率论中的收敛性注记

通过介绍初等概率论中的四种收敛性 ,揭示了它们之间的相互关系     

Degeneracy in the Maximum Likelihood Estimation of Univariate Gaussian Mixtures for Grouped Data and Behaviour of the EM Algorithm

Abstract.  In the context of the univariate Gaussian mixture with grouped data, it is shown that the global maximum of the likelihood may correspond to a situation where a Dirac lies in any non-empty interval. Existence of a domain of attraction near such a maximizer is discussed and we establish that the expectation-maximization (EM) iterates move extremely slowly inside this domain. These theoretical results are illustrated both by some Monte-Carlo experiments and by a real data set. To help practitioners identify and discard these potentially dangerous degenerate maximizers, a specific stopping rule for EM is proposed.     

二十一世纪东西文化趋近与中国文化创新

本文认为21世纪人类文化的大格局,仍将是多元并茂、互补共进,人类文化、东西文化发展的总趋势,必然是彼此逐渐走向趋近和融合,在趋近与融合中化解矛盾、避免冲突、互补互动、创新发展。汤因比的“世界统一论”、亨廷顿的“文明冲突论”,既不符合文化发展自身的逻辑,也是不现实的。中国文化在中西文化趋近与融合的大背景中,必然实现进一步的融合与创新,对解决人类面临的困境做出自己的贡献。     

声学各向异性介质中的S波

声学VTI介质是人为定义横波在对称轴方向的速度V_S0的一种模型。传统理论认为当V_S0=0时可以消除横波能量。论证声学VTI介质的存在，并讨论其特殊的性质，可以看到在声学VTI介质中SV波的相速度和群速度并不是恒为零。用高阶交错网格有限差分方法对不同的声学VTI介质模型进行全波场模拟，同时计算V_s0取不同值时的群速度和相速度x、z分量。通过对比分析得出波现象：SV波在垂直方向传播时其极化方向是平行于P波传播方向的；由于邻近方向能量的聚集，在对称轴附近SV波的振幅会有较大的值；P波和SV波的群速度的值在某些方向上可以很接近甚至相等。     

Consistent deconvolution in density estimation

Suppose we have n observations from X = Y + Z, where Z is a noise component with known distribution, and Y has an unknown density f. When the characteristic function of Z is nonzero almost everywhere, we show that it is possible to construct a density estimate f_n such that for all f, Iim_n| |=0.     

Institutionalizing Counter‐Memories of the U.S. Civil Rights Movement: The National Civil Rights Museum and an Application of the Interest‐Convergence Principle

During the post–Reconstruction era in the United States, white southerners marked the cultural landscape with monuments and memorials honoring the Confederate cause and its heroes. These racialized symbols enjoyed an undisputed claim to public squares and parks throughout the South. It was not until the late twentieth century that commemorations to the black freedom struggle were publicly supported. This analysis examines the institutionalization of counter‐memories of the civil rights movement in Memphis, Tennessee at the Lorraine Motel, the site of the assassination of Reverend Dr. Martin Luther King, Jr. The author draws on collective memory, cultural trauma, and social movements research as well as critical race theory to explain the creation of the National Civil Rights Museum. Using primary and secondary data sources the author examines how social memory agents, a changing political culture, and the passage of time mediated the cultural trauma of King's assassination and influenced the institutionalization of oppositional collective memories. Relying on Derrick Bell's interest‐convergence principle, the author concludes that the creation of this major memorial museum was a result of the convergence of white and black interests, specifically the economic and political interests of white elites and the cultural and political interests of black symbolic entrepreneurs.     

Approximating moments of continuous functions of random variables using Bernstein polynomials

Bernstein polynomials have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function $g\left(X\right)$ of a random variable $X$, and (2) proving Jensen’s inequality concerning a convex function without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the delta method, which is used to approximate the variance of $g\left(X\right)$ with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1).     

Local Estimation of the Conditional Stable Tail Dependence Function

We consider the local estimation of the stable tail dependence function when a random covariate is observed together with the variables of main interest. Our estimator is a weighted version of the empirical estimator adapted to the covariate framework. We provide the main asymptotic properties of our estimator, when properly normalized, in particular the convergence of the empirical process towards a tight centred Gaussian process. The finite sample performance of our estimator is illustrated on a small simulation study and on a dataset of air pollution measurements.