Implicit Numerical Simulation Of Stochastic Differential Equations With Jumps
Download Implicit Numerical Simulation Of Stochastic Differential Equations With Jumps full books in PDF, epub, and Kindle. Read online free Implicit Numerical Simulation Of Stochastic Differential Equations With Jumps ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Numerical Solution of Stochastic Differential Equations with Jumps in Finance
Author | : Eckhard Platen |
Publisher | : Springer Science & Business Media |
Total Pages | : 868 |
Release | : 2010-07-23 |
Genre | : Mathematics |
ISBN | : 364213694X |
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
Author | : Peter E. Kloeden |
Publisher | : Springer Science & Business Media |
Total Pages | : 666 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662126168 |
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
An Introduction to the Numerical Simulation of Stochastic Differential Equations
Author | : Desmond J. Higham |
Publisher | : SIAM |
Total Pages | : 293 |
Release | : 2021-01-28 |
Genre | : Mathematics |
ISBN | : 161197643X |
This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks. Although introductory, the book covers a range of modern research topics, including Itô versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlinear problems, multilevel Monte Carlo, approximation of double stochastic integrals, and tau leaping for chemical and biochemical reaction networks. An Introduction to the Numerical Simulation of Stochastic Differential Equations is appropriate for undergraduates and postgraduates in mathematics, engineering, physics, chemistry, finance, and related disciplines, as well as researchers in these areas. The material assumes only a competence in algebra and calculus at the level reached by a typical first-year undergraduate mathematics class, and prerequisites are kept to a minimum. Some familiarity with basic concepts from numerical analysis and probability is also desirable but not necessary.
Implicit Numerical Methods for Stiff Stochastic Differential Equations and Numerical Simulations of Stochastic Models
Author | : Tianhai Tian |
Publisher | : |
Total Pages | : 194 |
Release | : 2001 |
Genre | : Differential equations |
ISBN | : |
Reflecting Stochastic Differential Equations with Jumps and Applications
Author | : Situ Rong |
Publisher | : CRC Press |
Total Pages | : 228 |
Release | : 1999-08-05 |
Genre | : Mathematics |
ISBN | : 9781584881254 |
Many important physical variables satisfy certain dynamic evolution systems and can take only non-negative values. Therefore, one can study such variables by studying these dynamic systems. One can put some conditions on the coefficients to ensure non-negative values in deterministic cases. However, as a random process disturbs the system, the components of solutions to stochastic differential equations (SDE) can keep changing between arbitrary large positive and negative values-even in the simplest case. To overcome this difficulty, the author examines the reflecting stochastic differential equation (RSDE) with the coordinate planes as its boundary-or with a more general boundary. Reflecting Stochastic Differential Equations with Jumps and Applications systematically studies the general theory and applications of these equations. In particular, the author examines the existence, uniqueness, comparison, convergence, and stability of strong solutions to cases where the RSDE has discontinuous coefficients-with greater than linear growth-that may include jump reflection. He derives the nonlinear filtering and Zakai equations, the Maximum Principle for stochastic optimal control, and the necessary and sufficient conditions for the existence of optimal control. Most of the material presented in this book is new, including much new work by the author concerning SDEs both with and without reflection. Much of it appears here for the first time. With the application of RSDEs to various real-life problems, such as the stochastic population and neurophysiological control problems-both addressed in the text-scientists dealing with stochastic dynamic systems will find this an interesting and useful work.
Numerical Approximation of Stochastic Differential Equations Driven by Levy Motion with Infinitely Many Jumps
Author | : Ernest Jum |
Publisher | : |
Total Pages | : 128 |
Release | : 2015 |
Genre | : Brownian motion processes |
ISBN | : |
In this dissertation, we consider the problem of simulation of stochastic differential equations driven by pure jump Levy processes with infinite jump activity. Examples include, the class of stochastic differential equations driven by stable and tempered stable Levy processes, which are suited for modeling of a wide range of heavy tail phenomena. We replace the small jump part of the driving Levy process by a suitable Brownian motion, as proposed by Asmussen and Rosinski, which results in a jump-diffusion equation. We obtain Lp̳ [the space of measurable functions with a finite p-norm], for p greater than or equal to 2, and weak error estimates for the error resulting from this step. Combining this with numerical schemes for jump diffusion equations, we provide a good approximation method for the original stochastic differential equation that can also be implemented numerically. We complement these results with concrete error estimates and simulation.
Applied Stochastic Differential Equations
Author | : Simo Särkkä |
Publisher | : Cambridge University Press |
Total Pages | : 327 |
Release | : 2019-05-02 |
Genre | : Business & Economics |
ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Stochastic Integration with Jumps
Author | : Klaus Bichteler |
Publisher | : Cambridge University Press |
Total Pages | : 517 |
Release | : 2002-05-13 |
Genre | : Mathematics |
ISBN | : 0521811295 |
The complete theory of stochastic differential equations driven by jumps, their stability, and numerical approximation theories.
Modeling with Itô Stochastic Differential Equations
Author | : E. Allen |
Publisher | : Springer Science & Business Media |
Total Pages | : 239 |
Release | : 2007-03-08 |
Genre | : Mathematics |
ISBN | : 1402059531 |
This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.