Projection and Contraction Method for the Valuation of American Options

2015 ◽  
Vol 5 (1) ◽  
pp. 48-60 ◽  
Author(s):  
Haiming Song ◽  
Ran Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Inequality ◽  
American Options ◽  
Superior Performance ◽  
Contraction Method ◽  
Projection And Contraction Method ◽  
Black Scholes ◽  
The Matrix ◽  
Element Method

AbstractAn efficient numerical method is proposed for the valuation of American options via the Black-Scholes variational inequality. A far field boundary condition is employed to truncate the unbounded domain problem to produce the bounded domain problem with the associated variational inequality, to which our finite element method is applied. We prove that the matrix involved in the finite element method is symmetric and positive definite, and solve the discretized variational inequality by the projection and contraction method. Numerical experiments are conducted that demonstrate the superior performance of our method, in comparison with earlier methods.

Teaching the Finite Element Method As a Design Tool for Mechanical Engineering

1993 ◽  
Author(s):  
T. R. Grimm
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Solution Process ◽  
Thinking Skills ◽  
Design Tool ◽  
Basic Solution ◽  
The Finite Element Method ◽  
The Matrix ◽  
Analysis Of Results ◽  
Element Method

Abstract The importance of the finite element method as an engineering tool for design and analysis is emphasized in a senior level elective course taught at Michigan Technological University. The course emphasizes hands-on experience with computers and the pre- and post-analysis of results to establish confidence in solutions obtained. The students learn by using the finite element method to “solve” several design projects, rather than by being told about the method without significant actual experience. They also learn about the basis of the method, including formation of the matrix equations required and the numerical methods used in their solution. Intelligent use of the method requires that engineers understand both the mechanics of how to apply the method, i.e modeling requirements, and the limitations imposed by the basic solution process. The course provides the students with important experience in using the powerful finite element method as a design tool. It requires a strong background of fundamentals and stimulates the problem solving thinking skills so essential to industry.

Kinematics and Dynamics of a Multibody System of an Oilfield Pumping Unit by Means of Finite Element Method

1997 ◽  
Author(s):  
Si-zhu Zhou ◽  
Jacob Jen-Gwo Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Multibody System ◽  
Elastic System ◽  
Global Analysis ◽  
Oil Field ◽  
Kinematics And Dynamics ◽  
The Matrix ◽  
Pumping Unit ◽  
Element Method

Taking a multibody system of the oil field pumping unit into a multibody elastic system, this paper analyzes its kinematics and dynamics by means of finite element method, deduces the kinematics and dynamics function after doing the element’s and global analysis, and puts forward the procedures of this method, i.e., (1) dividing the system into elements; (2) calculating for the elements; (3) calculating the matrix of external force; (4) piling the element stiffness and mass matrixes up; and (5) solving the function. As an example, this paper illustrates the process of analyzing the multibody system of a PUMPING UNIT used in an oil field.

scholarly journals Hysteretic Behavior of Random Particulate Composites by the Stochastic Finite Element Method

Materials ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 2909 ◽  
Author(s):  
Damian Sokołowski ◽  
Marcin Kamiński
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cyclic Stretch ◽  
Hysteretic Behavior ◽  
Particulate Composites ◽  
Strain History ◽  
Stochastic Finite Element Method ◽  
Stochastic Finite Element ◽  
The Matrix ◽  
Element Method

Hysteretic behavior of random particulate composite was analyzed using the stochastic finite element method and three independent probabilistic formulations, i.e., generalized iterative stochastic perturbation technique of the tenth order, Monte-Carlo simulation, and semi-analytical method. This study was based on computational homogenization of the representative volume element (RVE), and its main focus was to demonstrate an influence of random stress in constitutive relation to the matrix on the deformation energies stored in the effective (homogenized) medium. This was done numerically for an increasing uncertainty of random matrix admissible stress with a Gaussian probability density function, for which the relations to the energies of the entire composite were approximated via the weighted least squares method algorithm. This composite was made of two phases, a hyper-elastic matrix exhibiting hysteretic behavior and a linear elastic spherical reinforcing particle located centrally in the RVE. The RVE was subjected to a cyclic stretch with an increasing amplitude, and computations of deformation energies were carried out using the finite element method system ABAQUS. A stress–strain history of the homogenized medium has been presented for the extreme and for the mean mechanical properties of the matrix to illustrate the random hysteresis of the given composite. The first four probabilistic moments and coefficients of the RVE deformation energy were determined and have been presented in addition to the input statistical scattering of the admissible stresses.

scholarly journals Stability Analysis of Symmetrical Rotor-Bearing Systems With Internal Damping Using Finite Element Method

1996 ◽  
Author(s):  
L. Forrai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Complex Form ◽  
Internal Damping ◽  
Bending Vibrations ◽  
Rotor Bearing ◽  
The Matrix ◽  
The Stability ◽  
Element Method

This paper deals with the stability analysis of self-excited bending vibrations of linear symmetrical rotor-bearing systems caused by internal damping using the finite element method. The rotor system consists of uniform circular Rayleigh shafts with internal viscous damping, symmetrical rigid disks, and discrete undamped isotropic bearings. By combining the sensitivity method and the matrix representation of the rotor dynamic equations in complex form to assess stability, it is proved theoretically that the stability threshold speed and the corresponding whirling speed coincide with the first forward critical speed regardless of the magnitude of the internal damping.

EXTENSION OF THE MORTAR FINITE ELEMENT METHOD TO A VARIATIONAL INEQUALITY MODELING UNILATERAL CONTACT

1999 ◽  
Vol 09 (02) ◽  
pp. 287-303 ◽  
Author(s):  
FAKER BEN BELGACEM ◽  
PATRICK HILD ◽  
PATRICK LABORDE
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Inequality ◽  
Unilateral Contact ◽  
Contact Conditions ◽  
Bootstrap Argument ◽  
Deformable Bodies ◽  
Mortar Finite Element Method ◽  
The One ◽  
Element Method

The purpose of this paper is to extend the mortar finite element method to handle the unilateral contact model between two deformable bodies. The corresponding variational inequality is approximated using finite element meshes which do not fit on the contact zone. The mortar technique allows one to match these independent discretizations of each solid and takes into account the unilateral contact conditions in a convenient way. By using an adaptation of Falk's lemma and a bootstrap argument, we give an upper bound of the convergence rate similar to the one already obtained for compatible meshes.

Finite Element Method in the Research on the Application of Contact Deformation

2012 ◽  
Vol 182-183 ◽  
pp. 1585-1589 ◽  
Author(s):  
Jia Jia Su ◽  
Jing Hu Chen
Keyword(s):  
Finite Element Method ◽  
Plastic Deformation ◽  
Finite Element ◽  
Stress State ◽  
Friction Coefficient ◽  
Contact Deformation ◽  
Matrix Surface ◽  
The Matrix ◽  
State Changes ◽  
Element Method

Wear is the matrix surface and plastic deformation as the basic factors of the phenomenon, this paper analyzed with abaqus finite element method friction deformation which stress. The results show that the stress state changes drastically with different friction coefficient and the distribution of plastic deformation regions also changes. The regions seriously damaged by friction lead to fatigue via plastic deformation, which is the main reason for material friction and then dislocation friction occurs.

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