Estimation In Stochastic Differential Equations
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Author | : Jaya P. N. Bishwal |
Publisher | : Springer |
Total Pages | : 271 |
Release | : 2007-09-26 |
Genre | : Mathematics |
ISBN | : 3540744487 |
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.
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.
Author | : Rong SITU |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2006-05-06 |
Genre | : Technology & Engineering |
ISBN | : 0387251758 |
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 | : M. Baadsgaard |
Publisher | : |
Total Pages | : 124 |
Release | : 1996 |
Genre | : |
ISBN | : |
Author | : Jaya P. N. Bishwal |
Publisher | : Springer Nature |
Total Pages | : 634 |
Release | : 2022-08-06 |
Genre | : Mathematics |
ISBN | : 3031038614 |
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Author | : Marianne Huebner |
Publisher | : |
Total Pages | : 248 |
Release | : 1993 |
Genre | : |
ISBN | : |
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
Author | : Lawrence C. Evans |
Publisher | : American Mathematical Soc. |
Total Pages | : 161 |
Release | : 2012-12-11 |
Genre | : Mathematics |
ISBN | : 1470410540 |
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).
Author | : Riccardo Cesari |
Publisher | : |
Total Pages | : 48 |
Release | : 1989 |
Genre | : Diffusion processes |
ISBN | : |
Author | : Stefano M. Iacus |
Publisher | : Springer Science & Business Media |
Total Pages | : 298 |
Release | : 2009-04-27 |
Genre | : Computers |
ISBN | : 0387758399 |
This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.