两资产亚式彩虹期权的定价研究

研究一种奇异路径依赖型期权——两资产亚式彩虹期权的定价问题.基于Black-Scholes期权定价模型的假设条件,利用无套利原理,构建了反映两资产亚式彩虹期权路径依赖特征的多因素定价模型.并结合边界条件,推导了基于两个标的资产的几何亚式彩虹期权的解析定价公式,借助它运用蒙特卡罗模拟法中减少变量技术对两资产算术亚式彩虹期权定价,得到了该期权更精确的估计值.     

亚式期权定价及其在期股激励上的应用

本文介绍了亚式期权在金融市场中所起的特殊作用,并就其定价问题进行讨论.介绍、分析了Monte Carlo模拟、几何平均近似法、二阶矩近似法、偏微分方程(PED)法、条件期望下限法等五种亚式期权的定价方法.针对当前企业期股激励制度存在的问题,本文提出将亚式期权运用于期股激励,并在后文给出了具体的计算实例.     

带跳市场中亚式期权的价格下界

亚式期权有两种类型,固定敲定价格亚式期权和浮动敲定价格亚式期权.它们的收益依附于标的资产有效期内的平均价格(算术平均),但是很难得到它们的闲形式的定价公式.借鉴Chen等在完备市场下对这两种亚式期权价格给出的下界的方法,给出了带跳市场中当标的资产价格为跳跃扩散过程时该两种期权价格的一个下界.     

关于亚式期权及其定价模型的研究

本文首先剖析了亚式期权的主要特征和价值生成机理.然后,利用无套利原理,创建了能够反映亚式期权路径依赖特征的多因素定价模型,并针对亚式期权的不同品种--平均价格型期权和平均执行价格型期权的定价分别进行了讨论.     

带跳市场中随机利率下的美式—亚式期权定价

在假设期权标的资产价格服从跳跃-扩散模型、利率遵循短期随机利率模型的基础上,运用总体最小二乘拟蒙特卡罗方法为美式-亚式期权定价,并将得到的定价结果和不带跳市场中美式-亚式期权的价格进行比较,数值结果表明,运用总体最小二乘拟蒙特卡罗方法得到的期权价格更好地反映了实际期权价格,并且该方法用于美式-亚式期权定价是合理的,时效性强,收敛速度快.     

服从CEV的几何亚式期权的定价研究

首先阐述了一种新型期权——标准几何亚式期权的涵义及其模型 ,介绍了 CEV(波动率弹性为常数 )的涵义 ;然后提出了二叉树方法在服从 CEV的几何亚式期权定价中的应用 ;最后给出了实例分析 ,验证了这种二叉树方法的有效性和收敛性     

基于随机波动率模型的路径依赖期权定价

在随机波动率框架下,对两种典型路径依赖期权进行定价.在期权标的资产价格的波动率是一个快速均值回归随机过程的假设下,研究了几何亚式看涨期权和浮动行权价回望看跌期权这两类路径依赖期权的定价问题.通过奇异摄动分析方法,对均值回归随机波动模型的偏微分方程进行分析得到关于期权近似价格的两个近似表示项,并推导出上述两种路径依赖期权的近似解析解.     

基于跳跃-扩散过程的一类亚式期权定价

在期权定价理论的研究中,一般都假设标的资产(设为股票)的价格服从几何布朗运动.然而在现实的金融市场上,当有重大信息到来时,便会对股票价格产生冲击,使其价格出现不连续的跳跃.考虑这一因素,在标的资产价格服从跳跃-扩散过程时,分别在完全市场与非完全市场上通过选择帐户折算变换与复制将一种亚式期权(考虑算术平均)定价问题进行简化为一种类似于欧式期权定价问题,然后运用Merton对冲风险方法得到原亚式期权的定价与套期保值策略.     

随机利率下亚式双币种期权的定价

在Black-Scholes的框架下,假设本国利率遵循短期随机利率模型(Vasicek模型),利用无套利方法,建立了敲定价和汇率分别为固定或浮动的3种情形下的亚式双币种期权的定价模型,运用偏微分方程的方法得到了这3种情形下期权的定价公式.然后,通过数值分析,讨论了期权关于时间变量的依赖行为.     

虹式亚洲期权定价

研究了一种奇异路径依赖型期权——具有虹式特征的亚洲期权的定价问题.基于Black-Scholes模型的假设条件, 利用多维ITO引理和无套利原理,构建了基于两个资产支付红利的虹式亚洲期权多因素路径依赖型期权定价模型,并结合边界条件,导出虹式几何平均亚洲看涨期权的解析定价公式以及虹式几何平均亚洲期权看涨-看跌平价关系式,以此为控制变量模拟计算虹式算术平均亚洲期权,数值实验表明虹式几何平均控制变量法有效地提高了蒙特卡罗模拟虹式算术平均亚洲期权定价的精确度.     

非线性微分代数方程的一种离散波形松弛算法

讨论用迭代方法求解微分代数方程。针对一类非线性微分代数方程连续时间波形松弛迭代格式,应用一般的单支方法和线性多步法,得到离散时间波形松弛迭代格式。在假定分裂函数满足Lipschitz条件的前提下,通过矩阵正则分裂和特殊矩阵相关性质的运用,获得离散波形松弛迭代的收敛性条件,拓展和改进了相关文献中的一些结果。     

一类两步方法的延迟依赖稳定性

讨论实系数延迟微分方程线性多步法的延迟依赖稳定性。重点致力于解析稳定区域和数值方法稳定区域的比较。对一类含有一个自由参数的两步方法，获得了数值稳定区域包含解析稳定区域的条件。数值试验证实了所获理论结果。     

Algebraic Stability of Multistep Runge-Kutta Methods

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Developing the methodology of TSI: From the oblique use of methods to creative design

During the last 13 years, a dialogue has been conducted in the Critical Systems literature on the subject of choice betwen methods. However, in the late 1980s and early 1990s, researchers went in two separate directions. One direction involved an exploration of the “creative design of methods.” This is when the problem situation is understood in terms of a series of systemically interrelated research questions, each of which might need to be addressed using a different method, or part of a method. A synthesis is generated that allows each individual research question to be addressed as part of a whole system of questions. The other research direction involved the development of “Total Systems Intervention” (TSI), a meta-methodology that, amongst other things, encourages the creative exploration of the problem situation prior to the choice of methods. One of the latest innovations in TSI is a theory of the “oblique” use of methods. This is the use of methods for purposes other than those they were originally designed for. However, it is argued here that all the case studies that have been subject to an “oblique” interpretation can be better explained if they are seen as examples of the creative design of methods. We can therefore bring together the two strands of research that have hitherto been pursued separately in the Critical Systems literature. it is suggested that TSI can be enhanced by an understanding of the creative design of methods because the latter allows us to explain the purposive, flexible, and responsive way in which TSI is most successfully used in practice.     

刚性Volterra泛函微分方程算法理论及高效算法

首先介绍刚性Volterra泛函微分方程的稳定性理论及其数值方法的B理论。这项工作为刚性延迟微分方程、刚性积分微分方程以及其它各种类型的刚性泛函微分方程的研究提供了统一的理论基础。其次以该理论为指针推荐高效算法，其中包括向后Euler方法、二阶BDF方法、并行多值混合方法及实特征值多步Runge—Kutta法。     

区间算法简介

近年来 ,国际上区间算法运用于计算科学和工程取得了一些显著成果 ,国内也开始了这方面的研究 .区间算法提出初衷是为了提高计算结果的可靠性 ,但是人们很快发现区间算法可以有更广泛的应用 ,如工程 ,金融等多方面 .区间算法对传统浮点算法进行了一个根本改革 ,它把计算的数存储为区间 ,并对这些区间进行运算 ,使避免浮点算法所产生的计算误差成为可能 .另外 ,区间算法使得区间参数能被直接包含在计算之中 ,这在实际应用里具有重要的意义 .区间算法是对浮点算法的一个有益补充 ,值得从事科技计算研究的工作者了解和应用.     

在反思中发展系统思维科学的理论

通过对传统的辩证思维方式与系统思维方式的比较分析 ,说明在反思中发展系统思维科学的理论的重要性     

IMPLICIT—EXPLICIT MULTISTEP FINITE ELEMENT METHODS FOR THE SEMICONDUCTOR DEVICE PROBLEM

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by the finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The optimal L^2-norm error estimates are derived.     

Systemic Approaches to Managing Across the Gap in the Public Sector: Results of an Action Research Programme

This paper tells the story and conclusions of a 1 year research project which took place over the calendar year of 2006. It was undertaken within a local government authority (or Local Authority—LA) in the UK. The specific research question to be answered was: “Can the application of systems methods in the LA aid Authority staff in developing and enhancing their professional practice?” A supplementary question arising was: “Can such learning be of wider value to other sections of the public sector (for example in other regions of local government or the health sector)?” In the process of the year 91 separate action research interactions took place. The research comes to three systemically linked findings: Firstly, LA middle managers are often caught between two realities ... strategic initiatives and operational demands. In the gap between these two realities they experience change in many guises but most critically in terms of government directives, ICT initiatives and restructuring. Despite this complexity managers did not appear to always have adequate tools to deal with issues arising in their context. Secondly, an assessment matrix developed originally at the Open University is a valuable tool for assessing the systemisism and reflective capacities of staff and, thirdly, a new, blended hybrid training programme to develop systemic reflective practitioners able to manage across the strategy/operations gap was developed and pilot tested in 2007. This programme shows signs of providing enhanced professional practice and, at the time of writing, is being further piloted with a view to establishing its wider applicability within the public sector.     

Construction of continuous time Markovian arrival processes

Markovian arrival processes were introduced by Neuts in 1979 (Neuts 1979) and have been used extensively in the stochastic modeling of queueing, inventory, reliability, risk, and telecommunications systems. In this paper, we introduce a constructive approach to define continuous time Markovian arrival processes. The construction is based on Poisson processes, and is simple and intuitive. Such a construction makes it easy to interpret the parameters of Markovian arrival processes. The construction also makes it possible to establish rigorously basic equations, such as Kolmogorov differential equations, for Markovian arrival processes, using only elementary properties of exponential distributions and Poisson processes. In addition, the approach can be used to construct continuous time Markov chains with a finite number of states