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Author : David Stahl
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.:/5 (17 download)
Download or read book Least Squares Monte Carlo for Backward Stochastic Differential Equations written by David Stahl and published by . This book was released on 2012 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : N El Karoui
Publisher : CRC Press
ISBN 13 : 9780582307339
Total Pages : 236 pages
Book Rating : 4.3/5 (73 download)
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Author : Andrew Bradford Leach
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (1 download)
Download or read book Monte Carlo Methods for Stochastic Differential Equations and Their Applications written by Andrew Bradford Leach and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce computationally efficient Monte Carlo methods for studying the statistics of stochastic differential equations in two distinct settings. In the first, we derive importance sampling methods for data assimilation when the noise in the model and observations are small. The methods are formulated in discrete time, where the "posterior" distribution we want to sample from can be analyzed in an accessible small noise expansion. We show that a "symmetrization" procedure akin to antithetic coupling can improve the order of accuracy of the sampling methods, which is illustrated with numerical examples. In the second setting, we develop "stochastic continuation" methods to estimate level sets for statistics of stochastic differential equations with respect to their parameters. We adapt Keller's Pseudo-Arclength continuation method to this setting using stochastic approximation, and generalized least squares regression. Furthermore, we show that the methods can be improved through the use of coupling methods to reduce the variance of the derivative estimates that are involved.
Author : Łukasz Delong
Publisher : Springer Science & Business Media
ISBN 13 : 1447153316
Total Pages : 285 pages
Book Rating : 4.4/5 (471 download)
Download or read book Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications written by Łukasz Delong and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Author : Deng Ding
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (13 download)
Download or read book A Regression-Based Numerical Method for Forward-Backward Stochastic Differential Equations written by Deng Ding and published by . This book was released on 2014 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a new class of basic functions based on characteristic functions to approximate two kinds of conditional expectations. we give the proofs and the error analysis of the approximations. In terms of such approximations, we employ a theta-discretization of time integrands for numerical solutions of forward-backward stochastic differential equations, and use Least-squares Monte Carlo simulations based on the basic functions. Numerical experiments are employed to show the algorithm available, and an empirical formula is pointed out for more general application.
Author : René Carmona
Publisher : Springer Science & Business Media
ISBN 13 : 3642257461
Total Pages : 478 pages
Book Rating : 4.6/5 (422 download)
Download or read book Numerical Methods in Finance written by René Carmona and published by Springer Science & Business Media. This book was released on 2012-03-23 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.
Author : Jianfeng Zhang
Publisher : Springer
ISBN 13 : 1493972561
Total Pages : 392 pages
Book Rating : 4.4/5 (939 download)
Download or read book Backward Stochastic Differential Equations written by Jianfeng Zhang and published by Springer. This book was released on 2017-08-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Author : Deng Ding
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (13 download)
Download or read book A Regression Method Based on Characteristic Functions for Numerical Solutions of Forward-Backward Stochastic Differential Equations written by Deng Ding and published by . This book was released on 2014 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop a theta-discretization of time integrands for numerical solutions of forward-backward stochastic differential equations, and suggest a new set of basic functions to the Least -squares Monte Carlo simulations. This set of basic functions bases on characteristic functions of transitional densities. Numerical experiments are employed by showing the algorithm available, and a empirical formula is pointed out for more general application.
Author : Steffen Meyer
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Monte-Carlo Methods for Backward Stochastic Differential Equations written by Steffen Meyer and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 1316510085
Total Pages : 327 pages
Book Rating : 4.3/5 (165 download)
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author : A. Stan Hurn
Publisher :
ISBN 13 : 9780732512279
Total Pages : 7 pages
Book Rating : 4.5/5 (122 download)
Download or read book Estimating the Parameters of Stochastic Differential Equations by Monte Carlo Methods written by A. Stan Hurn and published by . This book was released on 1995 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Emmanuel Gobet
Publisher : CRC Press
ISBN 13 : 149874625X
Total Pages : 216 pages
Book Rating : 4.4/5 (987 download)
Download or read book Monte-Carlo Methods and Stochastic Processes written by Emmanuel Gobet and published by CRC Press. This book was released on 2016-09-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.
Author : Giambattista Giacomin
Publisher : Springer
ISBN 13 : 3030150968
Total Pages : 649 pages
Book Rating : 4.0/5 (31 download)
Download or read book Stochastic Dynamics Out of Equilibrium written by Giambattista Giacomin and published by Springer. This book was released on 2019-06-30 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stemming from the IHP trimester "Stochastic Dynamics Out of Equilibrium", this collection of contributions focuses on aspects of nonequilibrium dynamics and its ongoing developments. It is common practice in statistical mechanics to use models of large interacting assemblies governed by stochastic dynamics. In this context "equilibrium" is understood as stochastically (time) reversible dynamics with respect to a prescribed Gibbs measure. Nonequilibrium dynamics correspond on the other hand to irreversible evolutions, where fluxes appear in physical systems, and steady-state measures are unknown. The trimester, held at the Institut Henri Poincaré (IHP) in Paris from April to July 2017, comprised various events relating to three domains (i) transport in non-equilibrium statistical mechanics; (ii) the design of more efficient simulation methods; (iii) life sciences. It brought together physicists, mathematicians from many domains, computer scientists, as well as researchers working at the interface between biology, physics and mathematics. The present volume is indispensable reading for researchers and Ph.D. students working in such areas.
Author : Jian Liang
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (13 download)
Download or read book Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative Pricing written by Jian Liang and published by . This book was released on 2020 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new forward-backward stochastic differential equation solver for highdimensional derivative pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonstrate the accuracy of our least square backward deep neural network solver and its capability to produce accurate prices for complex early exercise derivatives, such as callable yield notes. Our method can serve as a generic numerical solver for pricing derivatives across various asset groups, in particular, as an accurate means for pricing high-dimensional derivatives with early exercise features.
Author : Kossi Gnameho
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Numerical Solution for Backward SDEs written by Kossi Gnameho and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper deals with the numerical approximation of backward stochastic differential equations (BSDEs). We propose a new algorithm which is based on the regression later approach. Under some regularity assumptions, the solution of a forward backward stochastic differential equation (FBSDE) can be represented by the solution of a regular quasi-linear parabolic partial differential equation (PDE). On this basis, we have developed a probabilistic numerical regression called regression later algorithm based on the least squares Monte Carlo method and the previous connection between the quasi-linear parabolic partial differential equation and the FBSDE. The proposed algorithm yields good convergence results in practice. We will introduce briefly the theory of BSDEs, provide some general background on their studies and review the classical backward Euler-Maruyama scheme. Subsequently, we will describe the regression later algorithm, in further detail the algorithm and derive a convergence result. Finally, we will provides two numerical experiments to test the performance of the algorithm.
Author : Sangmeng Li
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (947 download)
Download or read book Multilevel Monte Carlo Simulation for Stochastic Differential Equations Driven by Lévy Processes written by Sangmeng Li and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christian Bender
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (744 download)
Download or read book Least-squares Monte Carlo for Backward SDEs written by Christian Bender and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
