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Mathematical Portfolio Theory and Analysis

Author: Siddhartha Pratim Chakrabarty

Publisher: Springer Nature

Published: 2023-02-18

Total Pages: 158

ISBN-13: 9811985448

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.

Introduction to Mathematical Portfolio Theory

Author: Mark S. Joshi

Publisher: Cambridge University Press

Published: 2013-07-11

Total Pages: 327

ISBN-13: 1107042313

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

Portfolio Theory and Arbitrage: A Course in Mathematical Finance

Author: Ioannis Karatzas

Publisher: American Mathematical Soc.

Published: 2021-08-12

Total Pages: 309

ISBN-13: 1470460149

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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.

Modern Portfolio Theory

Author: Jack Clark Francis

Publisher: John Wiley & Sons

Published: 2013-01-18

Total Pages: 576

ISBN-13: 1118417208

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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.

Stochastic Portfolio Theory

Author: E. Robert Fernholz

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 190

ISBN-13: 1475736991

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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.

Portfolio Theory and Arbitrage: A Course in Mathematical Finance

Author: Ioannis Karatzas

Publisher: American Mathematical Soc.

Published: 2021-09-20

Total Pages: 309

ISBN-13: 1470465981

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Portfolio Optimization and Performance Analysis

Author: Jean-Luc Prigent

Publisher: CRC Press

Published: 2007-05-07

Total Pages: 451

ISBN-13: 142001093X

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In answer to the intense development of new financial products and the increasing complexity of portfolio management theory, Portfolio Optimization and Performance Analysis offers a solid grounding in modern portfolio theory. The book presents both standard and novel results on the axiomatics of the individual choice in an uncertain framework, cont

Modern Portfolio Theory and Investment Analysis

Author: Edwin J. Elton

Publisher: John Wiley & Sons

Published: 2009-11-16

Total Pages: 748

ISBN-13: 0470388323

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An update of a classic book in the field, Modern Portfolio Theory examines the characteristics and analysis of individual securities as well as the theory and practice of optimally combining securities into portfolios. It stresses the economic intuition behind the subject matter while presenting advanced concepts of investment analysis and portfolio management. Readers will also discover the strengths and weaknesses of modern portfolio theory as well as the latest breakthroughs.

Mathematical Risk Analysis

Author: Ludger Rüschendorf

Publisher: Springer Science & Business Media

Published: 2013-03-12

Total Pages: 414

ISBN-13: 364233590X

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The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications. The first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.

Modern Portfolio Theory and Investment Analysis

Author: Edwin J. Elton

Publisher: John Wiley & Sons

Published: 2014-01-21

Total Pages: 754

ISBN-13: 1118469941

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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.