寡头垄断市场三度价格歧视动态博弈分析

对两寡头厂商2元市场用完全信息动态博弈的方法分析了实施三度价格歧视情形和统一定价情形的均衡产量,均衡价格和均衡总收益,并研究了这两种情形三个指标之间的关系.结果显示,在两个子市场的需求函数为线性需求的条件下,统一定价的市场均衡产量等于歧视定价的市场均衡产量;统一定价的均衡价格是歧视定价时两个子市场均衡价格的加权平均;统一定价的市场均衡总收益小于歧视定价的市场均衡总收益.     

分数布朗运动环境下上证50ETF期权定价的实证研究

合理的期权价格是期权交易的前提.基于上证50ETF期权的最新数据,运用经典的BlackScholes定价模型、蒙特卡洛模拟期权定价方法和分数布朗运动定价模型对上证50ETF期权价格进行实证研究.结果表明:分数布朗运动定价模型相比较经典的Black-Scholes定价模型和蒙特卡洛方法在接近期权的实际成交价格时均方误差和均方比例误差更小,能够较为准确地、有效地模拟出上证50ETF期权的价格,从而对投资者的期权交易行为具有一定的指导作用,也为国内其他品种的期权定价研究提供参考.     

简单可转换债券的定价——一种鞅方法

可转换债券作为债券和期权的混合体,其定价比债券和期权的定价都要复杂.本文用鞅方法讨论可转换债券的定价问题,给出了便于计算的类似于Black-Scholes模型的定价公式.但我们利用鞅方法使定价模型的推导更自然.基于这一定价模型,可转换债券的价格可分解为转换期权的价格和简单债券的价值之和.     

固定执行价格下回望看涨期权保险精算定价

利用保险精算方法,将期权定价问题转化为纯保费确定问题,根据股票价格过程的实际概率测度推导出了无风险利率为常数时,固定执行价格下回望看涨期权定价公式,验证了当标的资产的期望收益率等于无风险利率时,保险精算定价和风险中性定价的一致性.最后通过实例分析了保险精算价格和风险中性价格的差异,并利用Matlab编程得到了保险精算价格与标的资产期望收益率之间的关系.     

美式看跌期权的两点Geske-Johnson近似定价法

在分数Black-Scholes模型下,应用两点Geske-Johnson定价法推导连续支付红利为常数的美式看跌期权的近似公式.首先假定期权没有提前实施,其价格为对应欧式看跌期权的价格;再将期权的实施时刻指定为两个时刻,通过中性风险定价法推导价格公式,然后利用两点Geske-Johnson定价法得到美式看跌期权价格的近似公式.最后给出一个数值算例,结果显示Hurst参数和到期日对价格的影响.     

疫情环境下价格导向的防护物资最优生产分配机制研究

新型冠状病毒疫情导致防护物资匮乏,增加了医护人员受感染的风险.现构建了防护物资最优生产-分配-定价模型,并在此基础上提出了广义影子价格的概念,以此作为防护物资定价的参考和依据,通过价格引导生产型企业合理扩大生产规模,以解决当前防护物资短缺的困难.广义影子价格反映了企业产能提升成本等因素,相比传统影子价格更适用于为防护物资统一定价.另外,利用广义影子价格与拉格朗日乘子集合之间的联系,提出了一个线性规划模型用以计算广义影子价格.数值仿真结果说明了广义影子价格在防护物资定价上的适用性.     

一般均衡下基于产品市场和资本市场的单名CDS定价

次贷危机呼吁新的信用衍生品定价模型, 因此为存在产品市场和资本市场的经济结构建立一般均衡的单名CDS定价模型, 使用最优化求解一般均衡下的商品价格和CDS价格. 可以发现一般均衡的CDS定价具有资本市场和产品市场的因素, 这表示CDS的价格不再是由单纯的资本市场因素决定的, 而是由无风险利率、资本产出弹性、违约率、回收率同时决定的. 通过数量约束用模拟的方式研究多个均衡的动态变化, 发现违约风险的增加使得价格剧烈波动且市场交易萎缩. 在为以中国工商银行为参考资产的CDS定价过程中, 发现各种因素在不同的时期都可能成为定价的主要影响因素. 可以发现, 次贷危机的定价体系存在着信用调整问题和定价与实体经济脱节的问题. 可以认为, 一般均衡下基于产品市场和资本市场的单名CDS定价可以囊括多个市场的交叉影响, 为衍生品定价提供一个新的方向.     

疫情环境下价格导向的防护物资最优生产分配机制研究

新型冠状病毒疫情导致防护物资短缺,增加了医护人员受感染的风险.现构建了防护物资最优生产-分配-定价模型,并在此基础上提出了广义影子价格的概念,以此作为防护物资定价的参考和依据,通过价格引导生产型企业合理扩大生产规模,以解决当前防护物资短缺的困难.广义影子价格反映了企业产能提升成本等因素,相比传统影子价格更适用于为防护物资统一定价.另外,利用广义影子价格与拉格朗日乘子集合之间的联系,提出了一个线性规划模型用以计算广义影子价格.数值仿真结果说明了广义影子价格在防护物资定价上的适用性.     

隐私成本的模型研究

随着大数据时代的到来,数据的隐私、安全成本成为重要的研究课题.本文给出隐私定价模型的相关概念与问题描述,从价格和风险两方面探讨了隐私定价的相关参数和度量,包括隐私的内涵、内容和与价格相关的各种因素.隐私的定价机制应该包含选择合适的定价理论、定价模型,我们基于均衡价格理论,短期内个人信息价格是由供求均衡点决定,长期竞争均衡时价格等于长期平均成本的最低值,建立层次分析法、数学规划等数学模型方法解决隐私定价问题,并进行模拟计算.此外,对个人信息的市场供求关系、代际差异、政策法规与政府作用进行了讨论.     

基于LSMC模型的煤炭资源价值定价研究

煤炭资源价值定价可以抽象为一种美式期权定价问题.最小二乘蒙特卡洛模拟(LSMC)方法是解决美式期权定价问题的一个有效途径.详尽地分析了Cortazar等人的基于资源价格、利率和便利收益随机变动的三因素定价模型,利用向量Ito定理提出了三因素模型中价格、利率和便利收益变量的递推公式.对LSMC方法原理进行了细致的阐述,总结出实现LSMC方法的完整过程,并在Matlab环境下编制了LSMC算法实现程序,进行算例计算.算例结果表明,LSMC方法用于资源定价是有效可靠的.研究为煤炭资源价值定价提供了一个完整具有可操作性的工具.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by