Measure Probability And Mathematical Finance

Author : Guojun Gan,Chaoqun Ma,Hong Xie
Publisher : John Wiley & Sons
Page : 54 pages
File Size : 41,9 Mb
Release : 2014-04-07
Category : Mathematics
ISBN : 9781118831960

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Measure, Probability, and Mathematical Finance by Guojun Gan,Chaoqun Ma,Hong Xie Pdf

An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.

Author : Guojun Gan,Chaoqun Ma,Hong Xie
Publisher : Wiley
Page : 744 pages
File Size : 41,9 Mb
Release : 2014-04-18
Category : Mathematics
ISBN : 1118831977

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Measure, Probability, and Mathematical Finance by Guojun Gan,Chaoqun Ma,Hong Xie Pdf

Author : Jan Malczak,Ekkehard Kopp,Tomasz Zastawniak
Publisher : Cambridge University Press
Page : 197 pages
File Size : 49,6 Mb
Release : 2014
Category : Business & Economics
ISBN : 9781107002494

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Probability for Finance by Jan Malczak,Ekkehard Kopp,Tomasz Zastawniak Pdf

A rigorous, unfussy introduction to modern probability theory that focuses squarely on applications in finance.

Author : Pablo Koch Medina,Sandro Merino
Publisher : Birkhäuser
Page : 326 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880411

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Mathematical Finance and Probability by Pablo Koch Medina,Sandro Merino Pdf

This self-contained book presents the theory underlying the valuation of derivative financial instruments, which is becoming a standard part of the professional toolbox in the financial industry. It provides great insight into the underlying economic ideas in a very readable form, putting the reader in an excellent position to proceed to the more general continuous-time theory.

Author : Glenn Shafer,Vladimir Vovk
Publisher : John Wiley & Sons
Page : 438 pages
File Size : 41,5 Mb
Release : 2005-02-25
Category : Business & Economics
ISBN : 9780471461715

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Probability and Finance by Glenn Shafer,Vladimir Vovk Pdf

Provides a foundation for probability based on game theory rather than measure theory. A strong philosophical approach with practical applications. Presents in-depth coverage of classical probability theory as well as new theory.

Author : Ernst Eberlein,Jan Kallsen
Publisher : Springer Nature
Page : 774 pages
File Size : 52,5 Mb
Release : 2019-12-03
Category : Mathematics
ISBN : 9783030261061

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Mathematical Finance by Ernst Eberlein,Jan Kallsen Pdf

Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field. Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.

Author : Kai Lai Chung,Farid AitSahlia
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 48,6 Mb
Release : 2012-11-12
Category : Mathematics
ISBN : 9780387215488

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Elementary Probability Theory by Kai Lai Chung,Farid AitSahlia Pdf

This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales. From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

Author : Seán Dineen
Publisher : American Mathematical Soc.
Page : 323 pages
File Size : 55,5 Mb
Release : 2013-05-22
Category : Mathematics
ISBN : 9780821894903

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Probability Theory in Finance by Seán Dineen Pdf

The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of

Author : Glenn Shafer,Vladimir Vovk
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 47,7 Mb
Release : 2019-05-29
Category : Business & Economics
ISBN : 9780470903056

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Game-Theoretic Foundations for Probability and Finance by Glenn Shafer,Vladimir Vovk Pdf

Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University

Author : Ansgar Steland
Publisher : John Wiley & Sons
Page : 355 pages
File Size : 41,7 Mb
Release : 2012-06-21
Category : Business & Economics
ISBN : 9781118316566

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Financial Statistics and Mathematical Finance by Ansgar Steland Pdf

Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it considers various aspects of the application of statistical methods in finance and illustrates some of the many ways that statistical tools are used in financial applications. Financial Statistics and Mathematical Finance: Provides an introduction to the basics of financial statistics and mathematical finance. Explains the use and importance of statistical methods in econometrics and financial engineering. Illustrates the importance of derivatives and calculus to aid understanding in methods and results. Looks at advanced topics such as martingale theory, stochastic processes and stochastic integration. Features examples throughout to illustrate applications in mathematical and statistical finance. Is supported by an accompanying website featuring R code and data sets. Financial Statistics and Mathematical Finance introduces the financial methodology and the relevant mathematical tools in a style that is both mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, both graduate students and researchers in statistics, finance, econometrics and business administration will benefit from this book.

Author : Emanuela Rosazza Gianin,Carlo Sgarra
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 54,5 Mb
Release : 2014-02-10
Category : Mathematics
ISBN : 9783319013572

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Mathematical Finance: Theory Review and Exercises by Emanuela Rosazza Gianin,Carlo Sgarra Pdf

The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.

Author : Guojun Gan,Chaoqun Ma,Hong Xie
Publisher : John Wiley & Sons
Page : 54 pages
File Size : 44,6 Mb
Release : 2014-05-05
Category : Mathematics
ISBN : 9781118831984

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Measure, Probability, and Mathematical Finance by Guojun Gan,Chaoqun Ma,Hong Xie Pdf

An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.

Author : Arlie O. Petters,Xiaoying Dong
Publisher : Springer
Page : 483 pages
File Size : 51,7 Mb
Release : 2016-06-17
Category : Mathematics
ISBN : 9781493937837

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An Introduction to Mathematical Finance with Applications by Arlie O. Petters,Xiaoying Dong Pdf

This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.

Author : Patrick Billingsley
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 47,8 Mb
Release : 2012-01-20
Category : Mathematics
ISBN : 9781118341919

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Probability and Measure by Patrick Billingsley Pdf

Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniversary Edition builds on its strong foundation of measure theory and probability with Billingsley's unique writing style. In recognition of 35 years of publication, impacting tens of thousands of readers, this Anniversary Edition has been completely redesigned in a new, open and user-friendly way in order to appeal to university-level students. This book adds a new foreward by Steve Lally of the Statistics Department at The University of Chicago in order to underscore the many years of successful publication and world-wide popularity and emphasize the educational value of this book. The Anniversary Edition contains features including: An improved treatment of Brownian motion Replacement of queuing theory with ergodic theory Theory and applications used to illustrate real-life situations Over 300 problems with corresponding, intensive notes and solutions Updated bibliography An extensive supplement of additional notes on the problems and chapter commentaries Patrick Billingsley was a first-class, world-renowned authority in probability and measure theory at a leading U.S. institution of higher education. He continued to be an influential probability theorist until his unfortunate death in 2011. Billingsley earned his Bachelor's Degree in Engineering from the U.S. Naval Academy where he served as an officer. he went on to receive his Master's Degree and doctorate in Mathematics from Princeton University.Among his many professional awards was the Mathematical Association of America's Lester R. Ford Award for mathematical exposition. His achievements through his long and esteemed career have solidified Patrick Billingsley's place as a leading authority in the field and been a large reason for his books being regarded as classics. This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Like the previous editions, this Anniversary Edition is a key resource for students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.

Author : Ruth J. Williams
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 50,8 Mb
Release : 2006
Category : Business & Economics
ISBN : 9780821839034

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Introduction to the Mathematics of Finance by Ruth J. Williams Pdf

The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in thediscrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale,equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for acontinuous market model that generalizes the simple Black-Scholes model in several direct