Download Free Portfolio Theory And Arbitrage A Course In Mathematical Finance Book in PDF and EPUB Free Download. You can read online Portfolio Theory And Arbitrage A Course In Mathematical Finance and write the review.

This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called “Kelly” or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization. The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.
Designed as a self-contained text, this book covers a wide spectrum of topics on portfolio theory. It covers both the classical-mean-variance portfolio theory as well as non-mean-variance portfolio theory. The book covers topics such as optimal portfolio strategies, bond portfolio optimization and risk management of portfolios. In order to ensure that the book is self-contained and not dependent on any pre-requisites, the book includes three chapters on basics of financial markets, probability theory and asset pricing models, which have resulted in a holistic narrative of the topic. Retaining the spirit of the classical works of stalwarts like Markowitz, Black, Sharpe, etc., this book includes various other aspects of portfolio theory, such as discrete and continuous time optimal portfolios, bond portfolios and risk management. The increase in volume and diversity of banking activities has resulted in a concurrent enhanced importance of portfolio theory, both in terms of management perspective (including risk management) and the resulting mathematical sophistication required. Most books on portfolio theory are written either from the management perspective, or are aimed at advanced graduate students and academicians. This book bridges the gap between these two levels of learning. With many useful solved examples and exercises with solutions as well as a rigorous mathematical approach of portfolio theory, the book is useful to undergraduate students of mathematical finance, business and financial management.
This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called “Kelly” or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization. The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.
This concise yet comprehensive guide focuses on the mathematics of portfolio theory without losing sight of the finance.
With its emphasis on examples, exercises and calculations, this book suits advanced undergraduates as well as postgraduates and practitioners. It provides a clear treatment of the scope and limitations of mean-variance portfolio theory and introduces popular modern risk measures. Proofs are given in detail, assuming only modest mathematical background, but with attention to clarity and rigour. The discussion of VaR and its more robust generalizations, such as AVaR, brings recent developments in risk measures within range of some undergraduate courses and includes a novel discussion of reducing VaR and AVaR by means of hedging techniques. A moderate pace, careful motivation and more than 70 exercises give students confidence in handling risk assessments in modern finance. Solutions and additional materials for instructors are available at www.cambridge.org/9781107003675.
This book covers the characteristics and analysis of individual securities as well as the theory and practice of optimally combining securities into portfolios. Stressing the economic intuition behind the subject matter, this classic text pres-ents advanced concepts of investment analysis and portfolio management. It can be used for courses in both portfolio theory and in investment analysis that have an emphasis on portfolio the-ory. It can also be used in a course in investments where both portfolio analysis and security analysis are discussed. The authors' goal has been to make all the material in this text accessible to students of portfolio analysis and invest-ment management, both at the undergraduate and graduate levels while maintaining the rigor through the use of ap-pendices which can be used in conjunction with the text.
The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications.Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter.In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors.More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.
Using stereoscopic images and other novel pedagogical features, this book offers a comprehensive introduction to quantitative finance.