Pathwise Large Deviations of Stochastic Differential Equations with Applications to Finance PDF Download
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Author: Huizhong Wu
Publisher:
ISBN:
Category : Differential equations, Stochastic
Languages : en
Pages : 187
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Book Description
Author: Huizhong Wu
Publisher:
ISBN:
Category : Differential equations, Stochastic
Languages : en
Pages : 187
Get Book Here
Book Description
Author: Huizhong Wu
Publisher: LAP Lambert Academic Publishing
ISBN: 9783838360447
Category : Differential equations, Stochastic
Languages : en
Pages : 200
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Book Description
This work deals with the asymptotic behaviour of highly nonlinear stochastic differential equations, as well as linear and nonlinear functional differential equations. Both ordinary functional and neutral equations are analysed. In the first chapter, a class of nonlinear SDEs (mainly scaler equations) which satisfy the Law of the Iterated Logarithm is studied, and the results applied to a financial market model. The second chapter deals with a more general class of finite-dimensional nonlinear SDEs and SFDEs, employing comparison and time change methods, as well as martingale inequalities, to determine the almost sure rate of growth of the running maximum of functionals of the solution. The third chapter examines the exact almost sure rate of growth of the large deviations for affine SFDEs, and for equations with additive noise which are subject to relatively weak nonlinearities at infinity. The fourth chapter extends conventional conditons for existence and uniqueness of neutral functional differential equations to the stochastic case. The final chapter deals with large fluctuations of stochastic neutral functional differential equations.
Author: Huizhong Wu
Publisher:
ISBN:
Category :
Languages : en
Pages : 195
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Book Description
Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1316510085
Category : Business & Economics
Languages : en
Pages : 327
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Book Description
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author: Rong SITU
Publisher: Springer Science & Business Media
ISBN: 0387251758
Category : Technology & Engineering
Languages : en
Pages : 444
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Book Description
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.
Author: Carlos A. Braumann
Publisher: John Wiley & Sons
ISBN: 1119166063
Category : Mathematics
Languages : en
Pages : 299
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Book Description
A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, Itô or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: Contains a complete introduction to the basic issues of stochastic differential equations and their effective application Includes many examples in modelling, mainly from the biology and finance fields Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions Conveys the intuition behind the theoretical concepts Presents exercises that are designed to enhance understanding Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.
Author: Tusheng Zhang
Publisher: World Scientific
ISBN: 9814383570
Category : Business & Economics
Languages : en
Pages : 465
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Book Description
A collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. It covers the topics ranging from Markov processes, backward stochastic differential equations, stochastic partial differential equations, and stochastic control, to risk measure and risk theory.
Author: Erhabor Moses
Publisher: GRIN Verlag
ISBN: 3346113175
Category : Mathematics
Languages : en
Pages : 48
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Book Description
Seminar paper from the year 2019 in the subject Mathematics - Stochastics, grade: A, University of Benin, language: English, abstract: The following work tries to examine and provide soultions to an array of equations, most notably the Brownian motion, the Ito-integral and their application to finance. In the context of this work chapter one deals with the introduction, unique terms and notation and the usefulness in the project work. Chapter two deals with Brownian motion and the Ito integral, whereas chapter three deals with stochastic differential equations. Chapter four handles the application of stochastic differential equations to finance, and, finally, chapter five concludes the project.
Author: Andrés Boldori
Publisher:
ISBN:
Category :
Languages : en
Pages : 50
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Book Description
Author: Eckhard Platen
Publisher: Springer Science & Business Media
ISBN: 364213694X
Category : Mathematics
Languages : en
Pages : 868
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Book Description
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.
