Stochastic Differential Equations And Their Application In Finance An Overview

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Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance

Author : Carlos A. Braumann
Publisher : John Wiley & Sons
ISBN 13 : 1119166071
Total Pages : 303 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance by : Carlos A. Braumann

Download or read book Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance written by Carlos A. Braumann and published by John Wiley & Sons. This book was released on 2019-03-08 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Differential Equations

Author : Bernt Oksendal
Publisher : Springer Science & Business Media
ISBN 13 : 3662130505
Total Pages : 218 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Stochastic Differential Equations by : Bernt Oksendal

Download or read book Stochastic Differential Equations written by Bernt Oksendal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.

Applied Stochastic Differential Equations

Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 1316510085
Total Pages : 327 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä

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.

Introduction to Stochastic Calculus with Applications

Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner

Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

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

Author : Łukasz Delong
Publisher : Springer Science & Business Media
ISBN 13 : 1447153316
Total Pages : 285 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications by : Łukasz Delong

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.

Stochastic Differential Equations and Their Application in Finance. An Overview

Author : Erhabor Moses
Publisher : GRIN Verlag
ISBN 13 : 3346113175
Total Pages : 48 pages
Book Rating : 4.3/5 (461 download)

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Book Synopsis Stochastic Differential Equations and Their Application in Finance. An Overview by : Erhabor Moses

Download or read book Stochastic Differential Equations and Their Application in Finance. An Overview written by Erhabor Moses and published by GRIN Verlag. This book was released on 2020-02-14 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Forward-Backward Stochastic Differential Equations and their Applications

Author : Jin Ma
Publisher : Springer
ISBN 13 : 3540488316
Total Pages : 285 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Forward-Backward Stochastic Differential Equations and their Applications by : Jin Ma

Download or read book Forward-Backward Stochastic Differential Equations and their Applications written by Jin Ma and published by Springer. This book was released on 2007-04-24 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Differential Equations and Applications

Author : X Mao
Publisher : Elsevier
ISBN 13 : 085709940X
Total Pages : 445 pages
Book Rating : 4.8/5 (57 download)

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Book Synopsis Stochastic Differential Equations and Applications by : X Mao

Download or read book Stochastic Differential Equations and Applications written by X Mao and published by Elsevier. This book was released on 2007-12-30 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists. - Has been revised and updated to cover the basic principles and applications of various types of stochastic systems - Useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists

An Introduction to Stochastic Differential Equations

Author : Lawrence C. Evans
Publisher : American Mathematical Soc.
ISBN 13 : 1470410540
Total Pages : 161 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Stochastic Differential Equations by : Lawrence C. Evans

Download or read book An Introduction to Stochastic Differential Equations written by Lawrence C. Evans and published by American Mathematical Soc.. This book was released on 2012-12-11 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic. --Srinivasa Varadhan, New York University This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability. --George Papanicolaou, Stanford University This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically. --Alexander Lipton, Mathematical Finance Executive, Bank of America Merrill Lynch This short book provides a quick, but very readable introduction to stochastic differential equations, that is, to differential equations subject to additive ``white noise'' and related random disturbances. The exposition is concise and strongly focused upon the interplay between probabilistic intuition and mathematical rigor. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito stochastic calculus, and finally the theory of stochastic differential equations. The text also includes applications to partial differential equations, optimal stopping problems and options pricing. This book can be used as a text for senior undergraduates or beginning graduate students in mathematics, applied mathematics, physics, financial mathematics, etc., who want to learn the basics of stochastic differential equations. The reader is assumed to be fairly familiar with measure theoretic mathematical analysis, but is not assumed to have any particular knowledge of probability theory (which is rapidly developed in Chapter 2 of the book).

Numerical Solution of Stochastic Differential Equations

Author : Peter E. Kloeden
Publisher : Springer Science & Business Media
ISBN 13 : 3662126168
Total Pages : 666 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Numerical Solution of Stochastic Differential Equations by : Peter E. Kloeden

Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Rong SITU
Publisher : Springer Science & Business Media
ISBN 13 : 0387251758
Total Pages : 444 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Theory of Stochastic Differential Equations with Jumps and Applications by : Rong SITU

Download or read book Theory of Stochastic Differential Equations with Jumps and Applications written by Rong SITU and published by Springer Science & Business Media. This book was released on 2006-05-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Differential Equations

Author : Michael J. Panik
Publisher : John Wiley & Sons
ISBN 13 : 1119377404
Total Pages : 362 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Stochastic Differential Equations by : Michael J. Panik

Download or read book Stochastic Differential Equations written by Michael J. Panik and published by John Wiley & Sons. This book was released on 2017-03-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.

From Elementary Probability to Stochastic Differential Equations with MAPLE®

Author : Sasha Cyganowski
Publisher : Springer Science & Business Media
ISBN 13 : 3642561446
Total Pages : 323 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis From Elementary Probability to Stochastic Differential Equations with MAPLE® by : Sasha Cyganowski

Download or read book From Elementary Probability to Stochastic Differential Equations with MAPLE® written by Sasha Cyganowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. Based on measure theory, which is introduced as smoothly as possible, it provides practical skills in the use of MAPLE in the context of probability and its applications. It offers to graduates and advanced undergraduates an overview and intuitive background for more advanced studies.

Introduction to Stochastic Analysis

Author : Vigirdas Mackevicius
Publisher : John Wiley & Sons
ISBN 13 : 1118603249
Total Pages : 220 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Introduction to Stochastic Analysis by : Vigirdas Mackevicius

Download or read book Introduction to Stochastic Analysis written by Vigirdas Mackevicius and published by John Wiley & Sons. This book was released on 2013-02-07 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.

Stochastic Differential Equations in Infinite Dimensions

Author : Leszek Gawarecki
Publisher : Springer Science & Business Media
ISBN 13 : 3642161944
Total Pages : 300 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Stochastic Differential Equations in Infinite Dimensions by : Leszek Gawarecki

Download or read book Stochastic Differential Equations in Infinite Dimensions written by Leszek Gawarecki and published by Springer Science & Business Media. This book was released on 2010-11-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.

Backward Stochastic Differential Equations

Author : Jianfeng Zhang
Publisher : Springer
ISBN 13 : 1493972561
Total Pages : 392 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Backward Stochastic Differential Equations by : Jianfeng Zhang

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.

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications

Author : Rene Carmona
Publisher : SIAM
ISBN 13 : 1611974240
Total Pages : 263 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by : Rene Carmona

Download or read book Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications written by Rene Carmona and published by SIAM. This book was released on 2016-02-18 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.