Black Scholes Variational Inequalities
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Black Scholes Variational Inequalities
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Author : Karin Mautner
language : en
Publisher: VDM Publishing
Release Date : 2008-07-01
Black Scholes Variational Inequalities written by Karin Mautner and has been published by VDM Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-01 with Mathematics categories.
Numerical Methods For Fractional Black Scholes Equations And Variational Inequalities Governing Option Pricing
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Author : Wen Chen
language : en
Publisher:
Release Date : 2014
Numerical Methods For Fractional Black Scholes Equations And Variational Inequalities Governing Option Pricing written by Wen Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
[Truncated abstract] The aim of this thesis is to develop numerical methods for pricing options whose underlying follow a Levy process, establish convergence theories for these numerical methods and demonstrate the accuracy, effectiveness and practicality of the developed methods numerically. We first propose a second order finite difference method (FDM) for the one-dimensional fractional Black-Scholes (FBS) equation governing the valuation of European options on a single asset. We then show that both the continuous and discretized FBS equations are uniquely solvable and establish the convergence of the numerical solution generated by the FDM to the viscosity solution of the ontinuous FBS equation by proving that the FDM is consistent, stable and monotone. We then propose a power penalty method for a fractional-order dierential linear complementarity problem (LCP) arising in the valuation of American options on a single asset.
Numerical Treatment Of The Black Scholes Variational Inequality In Computational Finance
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Author : Karin Mautner
language : en
Publisher:
Release Date : 2006
Numerical Treatment Of The Black Scholes Variational Inequality In Computational Finance written by Karin Mautner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Mathematical Modeling And Methods Of Option Pricing
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Author : Lishang Jiang
language : en
Publisher: World Scientific
Release Date : 2005
Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
An Introduction To Variational Inequalities And Their Applications
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Author : David Kinderlehrer
language : en
Publisher: SIAM
Release Date : 2000-01-01
An Introduction To Variational Inequalities And Their Applications written by David Kinderlehrer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Mathematics categories.
Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.
Finite Dimensional Variational Inequalities And Complementarity Problems
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Author : Francisco Facchinei
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14
Finite Dimensional Variational Inequalities And Complementarity Problems written by Francisco Facchinei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-14 with Mathematics categories.
This is part one of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It covers the basic theory of finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.
Numerical Analysis Of Variational Inequalities
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Author : R. Trémolières
language : en
Publisher: Elsevier
Release Date : 2011-08-18
Numerical Analysis Of Variational Inequalities written by R. Trémolières and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
Numerical Analysis of Variational Inequalities
Stable Numerical Methodology For Variational Inequalities With Application In Quantitative Finance And Computational Mechanics
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Author : Davood Damircheli
language : en
Publisher:
Release Date : 2022
Stable Numerical Methodology For Variational Inequalities With Application In Quantitative Finance And Computational Mechanics written by Davood Damircheli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Coercivity is a characteristic property of the bilinear term in a weak form of a partial differential equation in both infinite space and the corresponding finite space utilized by a numerical scheme. This concept implies \textit{stability} and \textit{well-posedness} of the weak form in both the exact solution and the numerical solution. In fact, the loss of this property especially in finite dimension cases leads to instability of the numerical scheme. This phenomenon occurs in three major families of problems consisting of advection-diffusion equation with dominant advection term, elastic analysis of very thin beams, and associated plasticity and non-associated plasticity problems. There are two main paths to overcome the loss of coercivity, first manipulating and stabilizing a weak form to ensure that the discrete weak form is coercive, second using an automatically stable method to estimate the solution space such as the Discontinuous Petrov Galerkin (DPG) method in which the optimal test space is attained during the design of the method in such a way that the scheme keeps the coercivity inherently. In this dissertation, A stable numerical method for the aforementioned problems is proposed. A stabilized finite element method for the problem of migration risk problem which belongs to the family of the advection-diffusion problems is designed and thoroughly analyzed. Moreover, DPG method is exploited for a wide range of valuing option problems under the black-Scholes model including vanilla options, American options, Asian options, double knock barrier options where they all belong to family of advection-diffusion problem, and elastic analysis of Timoshenko beam theory. Besides, The problem of American option pricing, migration risk, and plasticity problems can be categorized as a free boundary value problem which has their extra complexity, and optimization theory and variational inequality are the main tools to study these families of the problems. Thus, an overview of the classic definition of variational inequalities and different tools and methods to study analytically and numerically this family of problems is provided and a novel adjoint sensitivity analysis of variational inequalities is proposed.
Lagrange Multiplier Approach To Variational Problems And Applications
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Author : Kazufumi Ito
language : en
Publisher: SIAM
Release Date : 2008-01-01
Lagrange Multiplier Approach To Variational Problems And Applications written by Kazufumi Ito and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.
Optimal Control Of Variational Inequalities
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Author : Viorel Barbu
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1984
Optimal Control Of Variational Inequalities written by Viorel Barbu and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.