三状态开关式波动率的美式看跌期权

本文研究三状态开关式波动率美式看跌期权的定价问题,假设波动率σ(t)取三个不同的值σ1,σ2,σ3,分别对应于股市中的熊市、振荡市和牛市,利用Δ对冲技巧得到了有三条自由边界(即最佳实施边界)的变分不等式模型;作为其应用,本文得到以下结果:若当前股票市场处于熊市(牛市),则在一定条件下,三状态开关式波动率美式看跌期权的最佳实施边界比标准美式看跌期权的最佳实施边界大(小),且三状态开关式波动率美式看跌期权的价格比标准美式看跌期权的价格低(高);若当前股票市场处于振荡市,则在一定条件下,三状态开关式波动率美式看跌期权的最佳实施边界比标准美式看跌期权的最佳实施边界小(大),且三状态开关式波动率美式看跌期权的价格比标准美式看跌期权的价格高(低)。     

Use of the Constrained Optimization Algorithms in Some Problems of Fracture Mechanics

In this paper we consider an algorithm of constrained optimization which arises from boundary variational principles of elastodynamics for bodies with cracks and unilateral constraints on the cracks edges. Variational formulation of unilateral contact problems with friction was considered, boundary variational functionals used with boundary integral equations were obtained and algorithm for solution of the unilateral contact problem with friction was developed. Some numerical results for 3-D elastodynamic unilateral contact problem for bodies with cracks are presented.     

压电材料变分原理逆问题的研究--动力学中的逆问题

研究了压电材料耦合动态场中Hamilton 型和Gurtin 型变分原理的逆问题。采用变积方法, 建立了各级变分原理和广义变分原理, 为建立横观各向同性压电材料的动力学有限元分析模型提供了依据。      

Free Boundary Problems in the Steel Industry

This paper considers two novel free boundary problems that emerge from modelling processes basic to steel manufacture. The first process concerns the spray cooling of hot steel sheet during the process of continuous casting. Here, an important practical consideration is the non-monotonicity of the measured heat transfer from the steel as a function of the steel temperature. In order to understand this phenomenon, a two-phase flow model is written down for the heating and vapourisation of the water spray. This model relies on a microscale analysis of droplet vapourisation and, in a steady state, it reduces to a coupled system of nonlinear ordinary differential equations for the spray temperature and water content. This system predicts the conditions for the existence or otherwise of a free boundary separating the two-phase region from a dry vapour layer close to the steel plate.The thickness of this vapour layer is determined by the solution of a generalised Stefan problem. The second process concerns the macroscopic modelling of pig .iron production in blast furnaces. In the simplest scenario, the blast furnace may be roughly divided into a porous solid region overlaying a hot high pressure gaseous zone. The gas reacts with the solid in a thin “intermediate region“ at the base of the solid region and it is in this intermediate region that the pig iron is produced. A free boundary model is proposed for the location of the intermediate region and its stability is investigated.     

On advancing front mesh generation in three dimensions

This paper deals with some aspects of unstructured mesh generation in three dimensions by the advancing front technique. In particular, the parameters used in the algorithm are characterized, and strategies that may be used to improve robustness are suggested. We also describe a method whereby structured tetrahedral meshes with exceptionally stretched elements adjacent to boundary surfaces may be produced. The suggested method can be combined with the advancing front concept in a natural way.     

耦合对流传热的Stokes流体形状优化设计

本文研究了耦合对流传热的Stokes流体中的形状优化问题.利用不可压缩的定常Stokes方程耦合对流传热的模型来描述流体的特性,运用形状导数方法分析依赖于区域的状态方程解的极小化问题.通过引入共轭状态方程,计算出目标函数的微分形式,并构造求解该形状优化问题的梯度型算法.数值实验的结果验证了所用方法的有效性和可行性.     

位移障碍下变分不等式问题的各向异性非协调有限元方法

本文研究位移障碍下二阶变分不等式问题在各向异性网格上的非协调有限元逼近。通过运用新的方法和技巧,得到了与正则网格剖分下相同的最优误差估计,从而扩展了有限元的应用范围。     

Variational formulations for boundary problems of electrostriction

Abstract

Variational formulations (or weak formulations) for nonlinear boundary problems of electrostriction are obtained by the variational theory of potential operators and the Vainberg theorem. The results achieved in this work can become the theoretical basis for the formulation of the numerical solutions of different scientific and engineering problems connected with the electrostrictive materials.     

各向异性外问题的非均匀网格的自然边界元法及其耦合法

本文对于无界区域上各向异性外问题提出了在椭圆边界非均匀网格上的自然边界元法及其与有限元法的耦合法,证明相应的收敛定理和误差估计式,并且在这两种方法中引入基于等分布原理的移动网格技巧.最后,通过数值结果表明了误差收敛理论的正确性以及所提方法和技巧的有效性.     

Free Boundary Determination in Nonlinear Diffusion

Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the lsqnonlin routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, instability is manifest in the derivative of the moving free surface, but not in the free surface itself nor in the concentration or temperature.     

Time-Dependent Reaction Coefficient Identification Problems with a Free Boundary

The determination of time-dependent reaction coefficients in free boundary heat transfer problems is numerically investigated. The additional data which provides a unique solution is given by the Stefan boundary condition and the heat moments. The finite difference method with the Crank-Nicolson scheme combined with a regularized nonlinear optimization is employed. The resulting nonlinear system of equations is solved numerically using the MATLAB toolbox routine lsqnonlin for minimizing the Tikhonov regularization functional. A discussion of the choice of regularization parameters is provided. Numerical results are presented and discussed.     

Modeling of textile composites with warp/weft frictional contact

A 2D modeling of textile composites is studied. The modeling is applicable to woven textile composites with flat fibers, used as reinforcing fibers of composite materials. Two 2D displacement fields are introduced, one for each layer of the fabric. The warp/weft interaction is taken into account by a nonlinear functional which characterizes the frictional contact. An explicit form of the warp/weft contact pressure is proposed. A numerical approximation of a solution of the variational problem is presented.     

变分方法在时标上一类边值问题中的应用

本文研究时标$mathbb T$上一类非自治的二阶周期边值问题周期解的存在性．我们综合利用临界点理论和变分方法,先利用变分方法将研究边值问题解的存在性问题转化为研究一个算子临界点问题,再借助于广义山路引理得到所研究边值问题存在至少一个周期解,所得结果在相应的微分方程,差分方程以及通常的时标上都是新的,作为应用,给出了一个例子验证了所得结论．     

Banach空间中关于变分不等式的收缩投影方法

在一致光滑的一致凸的Banach空间中,设计了一种收缩投影算法用以逼近变分不等式的解,并在紧算子减弱为连续算子的条件下,利用广义投影算子和K-K性质等技巧证明了该算法的强收敛性.所得结果是近期相关结果的改进与推广,其算法有重要应用.