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Author : Albert N. Shiryaev
Publisher : World Scientific
Page : 852 pages
File Size : 40,7 Mb
Release : 1999
Category : Business & Economics
ISBN : 9789810236052
Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos.
Author : Jia-An Yan
Publisher : Springer
Page : 403 pages
File Size : 40,9 Mb
Release : 2018-10-10
Category : Mathematics
ISBN : 9789811316579
This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems. The general theory of static risk measures, basic concepts and results on markets of semimartingale model, and a numeraire-free and original probability based framework for financial markets are also included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary knowledge, are presented.
Author : Steven Shreve
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 50,8 Mb
Release : 2005-06-28
Category : Mathematics
ISBN : 0387249680
Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance
Author : Fima C. Klebaner
Publisher : Imperial College Press
Page : 431 pages
File Size : 55,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945557
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.
Author : Jan Vecer
Publisher : CRC Press
Page : 342 pages
File Size : 44,9 Mb
Release : 2011-01-06
Category : Business & Economics
ISBN : 9781439812525
Unlike much of the existing literature, Stochastic Finance: A Numeraire Approach treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads to simpler pricing options for complex products, such as barrier, lookback, quant
Author : Hans Föllmer,Alexander Schied
Publisher : Walter de Gruyter GmbH & Co KG
Page : 608 pages
File Size : 40,5 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783110463453
This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures
Author : Nicolas Privault
Publisher : CRC Press
Page : 444 pages
File Size : 54,5 Mb
Release : 2013-12-20
Category : Business & Economics
ISBN : 9781466594029
Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading. With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.
Author : Marek Capiński,Ekkehard Kopp,Janusz Traple
Publisher : Cambridge University Press
Page : 187 pages
File Size : 44,7 Mb
Release : 2012-08-23
Category : Business & Economics
ISBN : 9781107002647
This book introduces key results essential for financial practitioners by means of concrete examples and a fully rigorous exposition.
Author : J. Michael Steele
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493054
Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH
Author : Martin Baxter,Andrew Rennie
Publisher : Cambridge University Press
Page : 252 pages
File Size : 41,5 Mb
Release : 1996-09-19
Category : Business & Economics
ISBN : 0521552893
A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.
Author : Ioannis Karatzas,Steven Shreve
Publisher : Springer
Page : 490 pages
File Size : 46,5 Mb
Release : 2014-03-27
Category : Mathematics
ISBN : 9781461209492
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
Author : Thomas Mikosch
Publisher : World Scientific
Page : 230 pages
File Size : 55,9 Mb
Release : 1998
Category : Mathematics
ISBN : 9810235437
Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.
Author : Damien Lamberton,Bernard Lapeyre
Publisher : CRC Press
Page : 254 pages
File Size : 51,6 Mb
Release : 2011-12-14
Category : Business & Economics
ISBN : 9781420009941
Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor, Introduction
Author : Masaaki Kijima
Publisher : CRC Press
Page : 343 pages
File Size : 47,9 Mb
Release : 2016-04-19
Category : Business & Economics
ISBN : 9781439884843
Financial engineering has been proven to be a useful tool for risk management, but using the theory in practice requires a thorough understanding of the risks and ethical standards involved. Stochastic Processes with Applications to Finance, Second Edition presents the mathematical theory of financial engineering using only basic mathematical tools
Author : Jean-François Le Gall
Publisher : Springer
Page : 273 pages
File Size : 47,6 Mb
Release : 2016-04-28
Category : Mathematics
ISBN : 9783319310893
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.