Portfolio Theory And Arbitrage A Course In Mathematical Finance

Author : Ioannis Karatzas,Constantinos Kardaras
Publisher : American Mathematical Soc.
Page : 309 pages
File Size : 47,7 Mb
Release : 2021-08-12
Category : Education
ISBN : 9781470460143

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Portfolio Theory and Arbitrage: A Course in Mathematical Finance by Ioannis Karatzas,Constantinos Kardaras Pdf

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.

Author : Ioannis Karatzas,Constantinos Kardaras
Publisher : American Mathematical Soc.
Page : 309 pages
File Size : 49,7 Mb
Release : 2021-09-20
Category : Education
ISBN : 9781470465988

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Portfolio Theory and Arbitrage: A Course in Mathematical Finance by Ioannis Karatzas,Constantinos Kardaras Pdf

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.

Author : Siddhartha Pratim Chakrabarty,Ankur Kanaujiya
Publisher : Springer Nature
Page : 158 pages
File Size : 52,6 Mb
Release : 2023-02-18
Category : Mathematics
ISBN : 9789811985447

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Mathematical Portfolio Theory and Analysis by Siddhartha Pratim Chakrabarty,Ankur Kanaujiya Pdf

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.

Author : E. Robert Fernholz
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 52,5 Mb
Release : 2013-04-17
Category : Business & Economics
ISBN : 9781475736991

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Stochastic Portfolio Theory by E. Robert Fernholz Pdf

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.

Author : Mark S. Joshi,Jane M. Paterson
Publisher : Cambridge University Press
Page : 327 pages
File Size : 40,5 Mb
Release : 2013-07-11
Category : Business & Economics
ISBN : 9781107042315

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Introduction to Mathematical Portfolio Theory by Mark S. Joshi,Jane M. Paterson Pdf

This concise yet comprehensive guide focuses on the mathematics of portfolio theory without losing sight of the finance.

Author : Edwin J. Elton,Martin J. Gruber,Stephen J. Brown,William N. Goetzmann
Publisher : John Wiley & Sons
Page : 754 pages
File Size : 48,8 Mb
Release : 2014-01-21
Category : Business & Economics
ISBN : 9781118469941

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Modern Portfolio Theory and Investment Analysis by Edwin J. Elton,Martin J. Gruber,Stephen J. Brown,William N. Goetzmann Pdf

An excellent resource for investors, Modern Portfolio Theory and Investment Analysis, 9th Edition examines the characteristics and analysis of individual securities as well as the theory and practice of optimally combining securities into portfolios. A chapter on behavioral finance is included, aimed to explore the nature of individual decision making. A chapter on forecasting expected returns, a key input to portfolio management, is also included. In addition, investors will find material on value at risk and the use of simulation to enhance their understanding of the field.

Author : Jack Clark Francis,Dongcheol Kim
Publisher : John Wiley & Sons
Page : 576 pages
File Size : 48,6 Mb
Release : 2013-01-22
Category : Business & Economics
ISBN : 9781118370520

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Modern Portfolio Theory, + Website by Jack Clark Francis,Dongcheol Kim Pdf

A through guide covering Modern Portfolio Theory as well as the recent developments surrounding it Modern portfolio theory (MPT), which originated with Harry Markowitz's seminal paper "Portfolio Selection" in 1952, has stood the test of time and continues to be the intellectual foundation for real-world portfolio management. This book presents a comprehensive picture of MPT in a manner that can be effectively used by financial practitioners and understood by students. Modern Portfolio Theory provides a summary of the important findings from all of the financial research done since MPT was created and presents all the MPT formulas and models using one consistent set of mathematical symbols. Opening with an informative introduction to the concepts of probability and utility theory, it quickly moves on to discuss Markowitz's seminal work on the topic with a thorough explanation of the underlying mathematics. Analyzes portfolios of all sizes and types, shows how the advanced findings and formulas are derived, and offers a concise and comprehensive review of MPT literature Addresses logical extensions to Markowitz's work, including the Capital Asset Pricing Model, Arbitrage Pricing Theory, portfolio ranking models, and performance attribution Considers stock market developments like decimalization, high frequency trading, and algorithmic trading, and reveals how they align with MPT Companion Website contains Excel spreadsheets that allow you to compute and graph Markowitz efficient frontiers with riskless and risky assets If you want to gain a complete understanding of modern portfolio theory this is the book you need to read.

Author : Diana R. Harrington
Publisher : Prentice Hall
Page : 242 pages
File Size : 51,9 Mb
Release : 1987
Category : Business & Economics
ISBN : UOM:39076000519178

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Modern Portfolio Theory, the Capital Asset Pricing Model, and Arbitrage Pricing Theory by Diana R. Harrington Pdf

Author : Holger Haldenwang,George Yuan,Zhiping Jiang
Publisher : European Alliance for Innovation
Page : 639 pages
File Size : 54,9 Mb
Release : 2023-04-14
Category : Business & Economics
ISBN : 9781631903939

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FFIT 2022 by Holger Haldenwang,George Yuan,Zhiping Jiang Pdf

The 2022 International Conference on Financial Innovation, FinTech and Information Technology (FFIT 2022), hosted by Shenzhen University of Technology and organized by the Financial Innovation and Fintech Research Center of Shenzhen University of Technology, was held on October 28-30, 2022 in Shenzhen, China. Due to the current COVID-19 pandemic and the strict travelling rules, it is still difficult to take international travel for all our attendees to participate in the conference. Therefore, FFIT 2022 was held as a hybrid event. FFIT 2022 brought together innovative academics and industrial experts in the field of Financial Innovation, Financial Technology and Information Technology to discuss the latest research results in this field.

Author : Anonim
Publisher : Bookboon
Page : 112 pages
File Size : 45,9 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9788776816056

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Portfolio Theory & Financial Analyses by Anonim Pdf

Author : Leonard C MacLean,William T Ziemba
Publisher : World Scientific Publishing Company
Page : 212 pages
File Size : 50,7 Mb
Release : 2016-09-29
Category : Electronic
ISBN : 9789814759366

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Problems in Portfolio Theory and the Fundamentals of Financial Decision Making by Leonard C MacLean,William T Ziemba Pdf

This book consists of invaluable introductions, tutorials and problems which are helpful for teaching purposes and have a very broad appeal and usage. The problems cover many aspects of static and dynamic portfolio theory as well as other important subjects such as arbitrage and asset pricing, utility theory, stochastic dominance, risk aversion and static portfolio theory, risk measures, dynamic portfolio theory and asset allocation. This material could be used with important books that cover these topics including MacLean-Ziemba's The Handbook of the Fundamentals of Financial Decision Making, and Ziemba-Vickson's Stochastic Optimization Models in Finance.

Author : T. Wake Epps
Publisher : John Wiley & Sons
Page : 448 pages
File Size : 41,9 Mb
Release : 2009-03-23
Category : Mathematics
ISBN : 0470455276

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Quantitative Finance by T. Wake Epps Pdf

A rigorous, yet accessible, introduction to essential topics in mathematical finance Presented as a course on the topic, Quantitative Finance traces the evolution of financial theory and provides an overview of core topics associated with financial investments. With its thorough explanations and use of real-world examples, this book carefully outlines instructions and techniques for working with essential topics found within quantitative finance including portfolio theory, pricing of derivatives, decision theory, and the empirical behavior of prices. The author begins with introductory chapters on mathematical analysis and probability theory, which provide the needed tools for modeling portfolio choice and pricing in discrete time. Next, a review of the basic arithmetic of compounding as well as the relationships that exist among bond prices and spot and forward interest rates is presented.? Additional topics covered include: Dividend discount models Markowitz mean-variance theory The Capital Asset Pricing Model Static?portfolio theory based on the expected-utility paradigm Familiar probability models for marginal distributions of returns and the dynamic behavior of security prices The final chapters of the book delve into the paradigms of pricing and present the application of martingale pricing in advanced models of price dynamics. Also included is a step-by-step discussion on the use of Fourier methods to solve for arbitrage-free prices when underlying price dynamics are modeled in realistic, but complex ways. Throughout the book, the author presents insight on current approaches along with comments on the unique difficulties that exist in the study of financial markets. These reflections illustrate the evolving nature of the financial field and help readers develop analytical techniques and tools to apply in their everyday work. Exercises at the end of most chapters progress in difficulty, and selected worked-out solutions are available in the appendix. In addition, numerous empirical projects utilize MATLAB® and Minitab® to demonstrate the mathematical tools of finance for modeling the behavior of prices and markets. Data sets that accompany these projects can be found via the book's FTP site. Quantitative Finance is an excellent book for courses in quantitative finance or financial engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for practitioners in related fields including engineering, finance, and economics.

Author : Ralf Korn,Elke Korn
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 45,6 Mb
Release : 2001
Category : Business & Economics
ISBN : 0821821237

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Option Pricing and Portfolio Optimization by Ralf Korn,Elke Korn Pdf

Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis: the Itô calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of purely mathematical topics are treated in extended "excursions" from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a self-contained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes as applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuous-time finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential.

Author : H. Kent Baker,Greg Filbeck
Publisher : Oxford University Press
Page : 802 pages
File Size : 41,6 Mb
Release : 2013-03-07
Category : Business & Economics
ISBN : 9780199829699

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Portfolio Theory and Management by H. Kent Baker,Greg Filbeck Pdf

Portfolio Theory and Management examines the foundations of portfolio management with the contributions of financial pioneers up to the latest trends. The book discusses portfolio theory and management both before and after the 2007-2008 financial crisis. It takes a global focus by highlighting cross-country differences and practices.

Author : Tomas Bjork
Publisher : Oxford University Press, USA
Page : 584 pages
File Size : 51,9 Mb
Release : 2020-01-16
Category : Arbitrage
ISBN : 9780198851615

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Arbitrage Theory in Continuous Time by Tomas Bjork Pdf

The fourth edition of this widely used textbook on pricing and hedging of financial derivatives now also includes dynamic equilibrium theory and continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, Arbitrage Theory in Continuous Time is designed for graduate students in economics and mathematics, and combines the 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. All concepts and ideas are discussed, not only from a mathematics point of view, but with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Bjork has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. This edition includes an entirely new section presenting dynamic equilibrium theory, covering unit net supply endowments models and the Cox-Ingersoll-Ross equilibrium factor model. Providing two full treatments of arbitrage theory-the classical delta hedging approach and the modern martingale approach-this book is written so that these approaches can be studied independently of each other, thus providing the less mathematically-oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action. This textbook is a natural choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in the market.