跳跃扩散过程的期权定价模型

假定股票价格的跳过程为计数过程,建立了股票价格服从跳扩散过程的行为模型.运用随机分析中的鞅方法,推导出了股票价格的跳过程为计数过程的欧式期权定价公式,推广了已有的结果.     

一类具有随机利率的跳扩散模型的期权定价

假定股票价格的跳过程为比Po isson过程更一般的跳过程一类特殊的更新过程,在风险中性的假设下,推导出了具有随机利率的跳扩散模型的欧式期权定价公式.从而推广了文[3]的结果.     

基于GMM方法跳聚集的短期利率模型参数估计

构建具有自我激励机制跳的短期利率模型,应用随机跳的强度来描述自我激励机制跳的过程,即当短期利率发生跳时,同时跳的强度也相应地发生跳,从而刻画跳的聚集现象.文章将以美国国债收益率作为研究目标,通过广义矩估计方法(GMM)给出了模型的参数估计和统计推断.借鉴随机微分算子Taylor展开方法,从理论上给出了精确的矩函数,并通过辅助粒子滤波器(APF)给出随机跳的强度估计.实证结果揭示了文章所构建的模型不仅能够很好地刻画极端事件对于短期利率的冲击,而且也很好地描述跳的聚集现象.此外,实证结果也表明了跳的强度可作为市场压力测试的一个重要指标.     

跳扩散模型下股价服从几何布朗运动的Esscher变换定价

考虑跳扩散模型下期权的Esscher变换定价,给出了Esscher变换下带跳的B-S矩生成函数和复合泊松过程下的矩生成函数,推导出跳扩散模型下期权的Esscher变换定价公式.     

具有随机利率的跳扩散模型下的脆弱期权的定价

本文研究了具有随机利率的跳扩散模型下考虑违约风险的欧式看涨和看跌期权的定价问题.当标的资产价值和交易对手的资产价值均服从含有共同跳跃的跳扩散模型,以及利率服从Vasicek模型时,利用跳扩散模型的Girsanov定理,给出了脆弱欧式看涨和看跌期权价格的显示表达式.     

资产价值服从跳-扩散过程的风险债券定价

作为对结构化模型和简化模型的改进,本文将结构化模型和简化模型两者融合后提出了一种特殊的跳-扩散过程.在假设公司价值服从这一类跳-扩散过程的情况下,建立了公司风险债券价值所满足的方程,并利用鞅方法得到了公司债券的定价公式.     

跳扩散过程下的保险商偿债率模型研究

本文研究了在有金融困境成本的情况下,带有跳扩散过程的保险商偿债率(SR)模型的问题.利用Girsanov定理进行测度变换的方法以及跳扩散过程下的看涨期权定价公式,获得了保险商终期收益的现值的结果.推广了不带跳扩散过程的保险商偿债率模型的结果.     

基于跳扩散模型欧式期权定价的条件二叉树方法

对股票价格的跳扩散模型进行了分析,在CRR二叉树期权定价模型的基础上考虑标的股票价格发生跳跃的情况,得出基于跳扩散过程的股票期权的条件二叉树定价模型,并且证明在极限情况下,该条件二叉树模型的期权定价公式趋于Merton的解析定价公式,数值试验证实该条件二叉树模型的有效性。     

跳扩散模型下美式期权的对称性

利用分析方法得到了跳扩散模型下美式看涨、看跌期权的价格和最佳实施边界间的对称性公式．美式看涨和看跌期权价格问的对称关系通常是利用概率理论得到,这里给出了这些结果在跳扩散模型下的另一种证明．此外,由本文所得结果和偏微分方程理论,可以得到跳扩散模型下美式看涨期权的最佳实施边界以及永久美式期权的若干性质．     

非参数模型的稳健跳点检测估计

非参数模型是统计学中常用的一类模型.在实际应用中,回归函数可能不是连续的,即在某些未知的位置上存在跳点.检测这些跳点对于回归函数的估计非常重要.本文基于B样条和众数估计,提出一个稳健跳点检测方法.然后利用检测出的跳点给出了回归函数的稳健有效估计量,并讨论了参数的选择.数值模拟和实例分析验证了所提方法在有限样本下的表现.     

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.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

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

正August 10-14,2015Beijin,China The 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     

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.     

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     

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     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.