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Author: Seán Dineen
Publisher: American Mathematical Soc.
ISBN: 0821894900
Category : Mathematics
Languages : en
Pages : 323
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Book Description
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: Seán Dineen
Publisher: American Mathematical Soc.
ISBN: 0821894900
Category : Mathematics
Languages : en
Pages : 323
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Book Description
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
Publisher: John Wiley & Sons
ISBN: 1118547934
Category : Business & Economics
Languages : en
Pages : 483
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Book Description
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: Kian Guan Lim
Publisher: World Scientific
ISBN: 9814307939
Category : Business & Economics
Languages : en
Pages : 405
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Book Description
This book provides a basic grounding in the use of probability to model random financial phenomena of uncertainty, and is targeted at an advanced undergraduate and graduate level. It should appeal to finance students looking for a firm theoretical guide to the deep end of derivatives and investments. Bankers and finance professionals in the fields of investments, derivatives, and risk management should also find the book useful in bringing probability and finance together. The book contains applications of both discrete time theory and continuous time mathematics, and is extensive in scope. Distribution theory, conditional probability, and conditional expectation are covered comprehensively, and applications to modeling state space securities under market equilibrium are made. Martingale is studied, leading to consideration of equivalent martingale measures, fundamental theorems of asset pricing, change of numeraire and discounting, risk-adjusted and forward-neutral measures, minimal and maximal prices of contingent claims, Markovian models, and the existence of martingale measures preserving the Markov property. Discrete stochastic calculus and multiperiod models leading to no-arbitrage pricing of contingent claims are also to be found in this book, as well as the theory of Markov Chains and appropriate applications in credit modeling. Measure-theoretic probability, moments, characteristic functions, inequalities, and central limit theorems are examined. The theory of risk aversion and utility, and ideas of risk premia are considered. Other application topics include optimal consumption and investment problems and interest rate theory.
Author: Glenn Shafer
Publisher: John Wiley & Sons
ISBN: 0471461717
Category : Business & Economics
Languages : en
Pages : 438
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Book Description
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: Guojun Gan
Publisher: John Wiley & Sons
ISBN: 1118831969
Category : Mathematics
Languages : en
Pages : 54
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Book Description
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: Jan Malczak
Publisher: Cambridge University Press
ISBN: 1107002494
Category : Business & Economics
Languages : en
Pages : 197
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Book Description
A rigorous, unfussy introduction to modern probability theory that focuses squarely on applications in finance.
Author: K. L. Chung
Publisher: Springer Science & Business Media
ISBN: 1475739737
Category : Mathematics
Languages : en
Pages : 332
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Book Description
This book provides an elementary introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. The fourth edition adds material related to mathematical finance, as well as expansions on stable laws and martingales.
Author: Svetlozar T. Rachev
Publisher: John Wiley & Sons
ISBN: 0470906324
Category : Business & Economics
Languages : en
Pages : 676
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Book Description
A comprehensive look at how probability and statistics is applied to the investment process Finance has become increasingly more quantitative, drawing on techniques in probability and statistics that many finance practitioners have not had exposure to before. In order to keep up, you need a firm understanding of this discipline. Probability and Statistics for Finance addresses this issue by showing you how to apply quantitative methods to portfolios, and in all matter of your practices, in a clear, concise manner. Informative and accessible, this guide starts off with the basics and builds to an intermediate level of mastery. • Outlines an array of topics in probability and statistics and how to apply them in the world of finance • Includes detailed discussions of descriptive statistics, basic probability theory, inductive statistics, and multivariate analysis • Offers real-world illustrations of the issues addressed throughout the text The authors cover a wide range of topics in this book, which can be used by all finance professionals as well as students aspiring to enter the field of finance.
Author: Kai Lai Chung
Publisher: Springer Science & Business Media
ISBN: 0387215484
Category : Mathematics
Languages : en
Pages : 411
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Book Description
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: Ioannis Karatzas
Publisher: Springer
ISBN: 1493968459
Category : Mathematics
Languages : en
Pages : 426
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Book Description
This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.
