Numerical Solution Of Stochastic Differential Equations With Jumps In Finance

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Numerical Solution of Stochastic Differential Equations with Jumps in Finance

Eckhard Platen,Nicola Bruti-Liberati
Numerical Solution of Stochastic Differential Equations with Jumps in Finance Book PDF

Author : Eckhard Platen,Nicola Bruti-Liberati
Publisher : Springer Science & Business Media
Page : 856 pages
File Size : 52,7 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9783642136948

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Numerical Solution of Stochastic Differential Equations with Jumps in Finance by Eckhard Platen,Nicola Bruti-Liberati Pdf

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Numerical Solution of Stochastic Differential Equations

Peter E. Kloeden,Eckhard Platen
Numerical Solution of Stochastic Differential Equations Book PDF

Author : Peter E. Kloeden,Eckhard Platen
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 43,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662126165

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Numerical Solution of Stochastic Differential Equations by Peter E. Kloeden,Eckhard Platen Pdf

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Theory of Stochastic Differential Equations with Jumps and Applications

Rong SITU
Theory of Stochastic Differential Equations with Jumps and Applications Book PDF

Author : Rong SITU
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 40,5 Mb
Release : 2006-05-06
Category : Technology & Engineering
ISBN : 9780387251752

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Theory of Stochastic Differential Equations with Jumps and Applications by Rong SITU Pdf

Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.

Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications

Łukasz Delong
Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications Book PDF

Author : Łukasz Delong
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 50,9 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781447153313

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Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications by Łukasz Delong Pdf

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.

Numerical Methods in Finance

L. C. G. Rogers,D. Talay
Numerical Methods in Finance Book PDF

Author : L. C. G. Rogers,D. Talay
Publisher : Cambridge University Press
Page : 348 pages
File Size : 43,5 Mb
Release : 1997-06-26
Category : Business & Economics
ISBN : 0521573548

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Numerical Methods in Finance by L. C. G. Rogers,D. Talay Pdf

Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.

Backward Stochastic Differential Equations

N El Karoui,Laurent Mazliak
Backward Stochastic Differential Equations Book PDF

Author : N El Karoui,Laurent Mazliak
Publisher : CRC Press
Page : 236 pages
File Size : 46,6 Mb
Release : 1997-01-17
Category : Mathematics
ISBN : 0582307333

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Backward Stochastic Differential Equations by N El Karoui,Laurent Mazliak Pdf

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.

Topics in Numerical Methods for Finance

Mark Cummins,Finbarr Murphy,John J.H. Miller
Topics in Numerical Methods for Finance Book PDF

Author : Mark Cummins,Finbarr Murphy,John J.H. Miller
Publisher : Springer
Page : 204 pages
File Size : 53,7 Mb
Release : 2012-07-16
Category : Mathematics
ISBN : 1461434343

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Topics in Numerical Methods for Finance by Mark Cummins,Finbarr Murphy,John J.H. Miller Pdf

Presenting state-of-the-art methods in the area, the book begins with a presentation of weak discrete time approximations of jump-diffusion stochastic differential equations for derivatives pricing and risk measurement. Using a moving least squares reconstruction, a numerical approach is then developed that allows for the construction of arbitrage-free surfaces. Free boundary problems are considered next, with particular focus on stochastic impulse control problems that arise when the cost of control includes a fixed cost, common in financial applications. The text proceeds with the development of a fear index based on equity option surfaces, allowing for the measurement of overall fear levels in the market. The problem of American option pricing is considered next, applying simulation methods combined with regression techniques and discussing convergence properties. Changing focus to integral transform methods, a variety of option pricing problems are considered. The COS method is practically applied for the pricing of options under uncertain volatility, a method developed by the authors that relies on the dynamic programming principle and Fourier cosine series expansions. Efficient approximation methods are next developed for the application of the fast Fourier transform for option pricing under multifactor affine models with stochastic volatility and jumps. Following this, fast and accurate pricing techniques are showcased for the pricing of credit derivative contracts with discrete monitoring based on the Wiener-Hopf factorisation. With an energy theme, a recombining pentanomial lattice is developed for the pricing of gas swing contracts under regime switching dynamics. The book concludes with a linear and nonlinear review of the arbitrage-free parity theory for the CDS and bond markets.

Topics in Numerical Methods for Finance

Mark Cummins,Finbarr Murphy,John J.H. Miller
Topics in Numerical Methods for Finance Book PDF

Author : Mark Cummins,Finbarr Murphy,John J.H. Miller
Publisher : Springer Science & Business Media
Page : 213 pages
File Size : 51,8 Mb
Release : 2012-07-15
Category : Mathematics
ISBN : 9781461434337

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Topics in Numerical Methods for Finance by Mark Cummins,Finbarr Murphy,John J.H. Miller Pdf

Presenting state-of-the-art methods in the area, the book begins with a presentation of weak discrete time approximations of jump-diffusion stochastic differential equations for derivatives pricing and risk measurement. Using a moving least squares reconstruction, a numerical approach is then developed that allows for the construction of arbitrage-free surfaces. Free boundary problems are considered next, with particular focus on stochastic impulse control problems that arise when the cost of control includes a fixed cost, common in financial applications. The text proceeds with the development of a fear index based on equity option surfaces, allowing for the measurement of overall fear levels in the market. The problem of American option pricing is considered next, applying simulation methods combined with regression techniques and discussing convergence properties. Changing focus to integral transform methods, a variety of option pricing problems are considered. The COS method is practically applied for the pricing of options under uncertain volatility, a method developed by the authors that relies on the dynamic programming principle and Fourier cosine series expansions. Efficient approximation methods are next developed for the application of the fast Fourier transform for option pricing under multifactor affine models with stochastic volatility and jumps. Following this, fast and accurate pricing techniques are showcased for the pricing of credit derivative contracts with discrete monitoring based on the Wiener-Hopf factorisation. With an energy theme, a recombining pentanomial lattice is developed for the pricing of gas swing contracts under regime switching dynamics. The book concludes with a linear and nonlinear review of the arbitrage-free parity theory for the CDS and bond markets.

Applied Stochastic Differential Equations

Simo Särkkä,Arno Solin
Applied Stochastic Differential Equations Book PDF

Author : Simo Särkkä,Arno Solin
Publisher : Cambridge University Press
Page : 327 pages
File Size : 48,9 Mb
Release : 2019-05-02
Category : Business & Economics
ISBN : 9781316510087

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Applied Stochastic Differential Equations by Simo Särkkä,Arno Solin Pdf

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Forward-Backward Stochastic Differential Equations and their Applications

Jin Ma,Jiongmin Yong
Forward Backward Stochastic Differential Equations and their Applications Book PDF

Author : Jin Ma,Jiongmin Yong
Publisher : Springer
Page : 278 pages
File Size : 47,5 Mb
Release : 2007-04-24
Category : Mathematics
ISBN : 9783540488316

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Forward-Backward Stochastic Differential Equations and their Applications by Jin Ma,Jiongmin Yong Pdf

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

Numerical Solution of SDE Through Computer Experiments

Peter Eris Kloeden,Eckhard Platen,Henri Schurz
Numerical Solution of SDE Through Computer Experiments Book PDF

Author : Peter Eris Kloeden,Eckhard Platen,Henri Schurz
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642579134

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Numerical Solution of SDE Through Computer Experiments by Peter Eris Kloeden,Eckhard Platen,Henri Schurz Pdf

This book provides an easily accessible, computationally-oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations. It also creates an intuitive understanding of the necessary theoretical background. Software containing programs for over 100 problems is available online.

Numerical Methods in Computational Finance

Daniel J. Duffy
Numerical Methods in Computational Finance Book PDF

Author : Daniel J. Duffy
Publisher : John Wiley & Sons
Page : 551 pages
File Size : 49,8 Mb
Release : 2022-03-14
Category : Business & Economics
ISBN : 9781119719724

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Numerical Methods in Computational Finance by Daniel J. Duffy Pdf

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.

Asymptotic Analysis for Functional Stochastic Differential Equations

Jianhai Bao,George Yin,Chenggui Yuan
Asymptotic Analysis for Functional Stochastic Differential Equations Book PDF

Author : Jianhai Bao,George Yin,Chenggui Yuan
Publisher : Springer
Page : 151 pages
File Size : 52,7 Mb
Release : 2016-11-19
Category : Mathematics
ISBN : 9783319469799

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Asymptotic Analysis for Functional Stochastic Differential Equations by Jianhai Bao,George Yin,Chenggui Yuan Pdf

This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.

Financial Modelling with Jump Processes

Peter Tankov
Financial Modelling with Jump Processes Book PDF

Author : Peter Tankov
Publisher : CRC Press
Page : 552 pages
File Size : 47,6 Mb
Release : 2003-12-30
Category : Business & Economics
ISBN : 9781135437947

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Financial Modelling with Jump Processes by Peter Tankov Pdf

WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Numerical Approximation of Ordinary Differential Problems

Raffaele D'Ambrosio
Numerical Approximation of Ordinary Differential Problems Book PDF

Author : Raffaele D'Ambrosio
Publisher : Springer Nature
Page : 391 pages
File Size : 48,6 Mb
Release : 2023-09-26
Category : Mathematics
ISBN : 9783031313431

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Numerical Approximation of Ordinary Differential Problems by Raffaele D'Ambrosio Pdf

This book is focused on the numerical discretization of ordinary differential equations (ODEs), under several perspectives. The attention is first conveyed to providing accurate numerical solutions of deterministic problems. Then, the presentation moves to a more modern vision of numerical approximation, oriented to reproducing qualitative properties of the continuous problem along the discretized dynamics over long times. The book finally performs some steps in the direction of stochastic differential equations (SDEs), with the intention of offering useful tools to generalize the techniques introduced for the numerical approximation of ODEs to the stochastic case, as well as of presenting numerical issues natively introduced for SDEs. The book is the result of an intense teaching experience as well as of the research carried out in the last decade by the author. It is both intended for students and instructors: for the students, this book is comprehensive and rather self-contained; for the instructors, there is material for one or more monographic courses on ODEs and related topics. In this respect, the book can be followed in its designed path and includes motivational aspects, historical background, examples and a software programs, implemented in Matlab, that can be useful for the laboratory part of a course on numerical ODEs/SDEs. The book also contains the portraits of several pioneers in the numerical discretization of differential problems, useful to provide a framework to understand their contributes in the presented fields. Last, but not least, rigor joins readability in the book.