Download or read book Optimal Portfolios written by Ralf Korn and published by World Scientific. This book was released on 1997 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.
Download or read book Optimal Portfolios Stochastic Models For Optimal Investment And Risk Management In Continuous Time written by Ralf Korn and published by World Scientific. This book was released on 1997-11-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.Stress is laid on rigorous mathematical presentation and clear economic interpretations while technicalities are kept to the minimum. The underlying mathematical concepts will be provided. No a priori knowledge of stochastic calculus, stochastic control or partial differential equations is necessary (however some knowledge in stochastics and calculus is needed).
Download or read book Optimal Portfolios with Stochastic Interest Rates and Defaultable Assets written by Holger Kraft and published by Springer Science & Business Media. This book was released on 2004-04-13 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The continuous-time portfolio problem consists of finding the optimal investment strategy of an investor. In the classical Merton problem the investor can allocate his funds to a riskless savings account and risky assets. However, to get explicit results, it is assumed that the interest rates are deterministic and that the assets are default free. In this monograph both assumptions are weakened: The author analyzes and solves portfolio problems with stochastic interest rates and with defaultable assets. Besides, he briefly discusses how portfolio problems with foreign assets can be handled. The focus of the monograph is twofold: On the one hand, the economical problems are carefully explained, on the other hand their formal solution is rigorously presented. For this reason the text should be of interest to researchers with a Finance background as well as to researchers with a more formal background who would like to see how mathematics is applied to portfolio theory. TOC:Preliminaries from Stochastics.- Optimal Portfolios with Stochastic Interest Rates.- Elasticity Approach to Portfolio Optimization.- Barrier Derivatives with Curved Boundaries.- Optimal Portfolios with Dafaultable Assets - A Firm Value Approach.- References.- Abbreviations.- Notations.
Download or read book Stochastic Optimization Models in Finance written by W. T. Ziemba and published by World Scientific. This book was released on 2006 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems. Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever. Sample Chapter(s). Chapter 1: Expected Utility Theory (373 KB). Contents: Mathematical Tools: Expected Utility Theory; Convexity and the Kuhn-Tucker Conditions; Dynamic Programming; Qualitative Economic Results: Stochastic Dominance; Measures of Risk Aversion; Separation Theorems; Static Portfolio Selection Models: Mean-Variance and Safety First Approaches and Their Extensions; Existence and Diversification of Optimal Portfolio Policies: Effects of Taxes on Risk Taking; Dynamic Models Reducible to Static Models: Models That Have a Single Decision Point; Risk Aversion over Time Implies Static Risk Aversion; Myopic Portfolio Policies; Dynamic Models: Two-Period Consumption Models and Portfolio Revision; Models of Optimal Capital Accumulation and Portfolio Selection; Models of Option Strategy; The Capital Growth Criterion and Continuous-Time Models. Readership: Postdoctoral and graduate students, researchers, academics, and professionals interested in portfolio theory and stochastic optimization.
Download or read book Mathematical Portfolio Theory and Analysis written by Siddhartha Pratim Chakrabarty and published by Springer Nature. This book was released on 2023-02-18 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied Stochastic Control of Jump Diffusions written by Bernt Øksendal and published by Springer Science & Business Media. This book was released on 2007-04-26 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Download or read book Mathematical Systems Theory in Biology Communications Computation and Finance written by Joachim Rosenthal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.
Download or read book OPTIMIZATION AND OPERATIONS RESEARCH Volume IV written by Ulrich Derigs and published by EOLSS Publications. This book was released on 2009-04-15 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization and Operations Research is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Optimization and Operations Research is organized into six different topics which represent the main scientific areas of the theme: 1. Fundamentals of Operations Research; 2. Advanced Deterministic Operations Research; 3. Optimization in Infinite Dimensions; 4. Game Theory; 5. Stochastic Operations Research; 6. Decision Analysis, which are then expanded into multiple subtopics, each as a chapter. These four volumes are aimed at the following five major target audiences: University and College students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.
Download or read book Handbook of Asset and Liability Management written by Stavros A. Zenios and published by Elsevier. This book was released on 2007-08-08 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series presents an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. It is fitting that the series Handbooks in Finance devotes a handbook to Asset and Liability Management. Volume 2 focuses on applications and case studies in asset and liability management.The growth in knowledge about practical asset and liability modeling has followed the popularity of these models in diverse business settings. This volume portrays ALM in practice, in contrast to Volume 1, which addresses the theories and methodologies behind these models. In original articles practitioners and scholars describe and analyze models used in banking, insurance, money management, individual investor financial planning, pension funds, and social security. They put the traditional purpose of ALM, to control interest rate and liquidity risks, into rich and broad-minded frameworks. Readers interested in other business settings will find their discussions of financial institutions both instructive and revealing. * Focuses on pragmatic applications * Relevant to a variety of risk-management industries* Analyzes models used in most financial sectors
Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
Download or read book Continuous time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.
Download or read book Statistics of Financial Markets written by Jürgen Franke and published by Springer Science & Business Media. This book was released on 2010-11-22 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistics of Financial Markets offers a vivid yet concise introduction to the growing field of statistical application in finance. The reader will learn the basic methods of evaluating option contracts, analysing financial time series, selecting portfolios and managing risks making realistic assumptions of the market behaviour. The focus is both on the fundamentals of mathematical finance and financial time series analysis and on applications to given problems of financial markets, thus making the book the ideal basis for lecturers, seminars and crash courses on the topic. For the third edition the book has been updated and extensively revised. Several new aspects have been included: new chapters on long memory models, copulae and CDO valuation. Practical exercises have been added, the solutions of which are provided in the book by S. Borak, W. Härdle and B. Lopez Cabrera (2010) ISBN 978-3-642-11133-4. “Both R and Matlab Code, together with the data, can be downloaded by clicking on the Additional Information tab labeled “R and Matlab Code,” which you will find on the right-hand side of the webpage.”
Download or read book Numerical Methods in Finance and Economics written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.
Download or read book Stochastic Finance written by Albert N. Shiryaev and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Black, Scholes, and Merton in the field of financial mathematics, research has led to the rapid development of a substantial body of knowledge, with plenty of applications to the common functioning of the world’s financial institutions. Mathematics, as the language of science, has always played a role in the development of knowledge and technology. Presently, the high-tech character of modern business has increased the need for advanced methods, which rely to a large extent on mathematical techniques. It has become essential for the financial analyst to possess a high degree of proficiency in these mathematical techniques.
Download or read book Advanced Asset Pricing Theory written by Chenghu Ma and published by World Scientific. This book was released on 2011 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad introduction to modern asset pricing theory. The theory is self-contained and unified in presentation. Both the no-arbitrage and the general equilibrium approaches of asset pricing theory are treated coherently within the general equilibrium framework. It fills a gap in the body of literature on asset pricing for being both advanced and comprehensive. The absence of arbitrage opportunities represents a necessary condition for equilibrium in the financial markets. However, the absence of arbitrage is not a sufficient condition for establishing equilibrium. These interrelationships are overlooked by the proponents of the no-arbitrage approach to asset pricing.This book also tackles recent advancement on inversion problems raised in asset pricing theory, which include the information role of financial options and the information content of term structure of interest rates and interest rates contingent claims.The inclusion of the proofs and derivations to enhance the transparency of the underlying arguments and conditions for the validity of the economic theory made it an ideal advanced textbook or reference book for graduate students specializing in financial economics and quantitative finance. The detailed explanations will capture the interest of the curious reader, and it is complete enough to provide the necessary background material needed to delve deeper into the subject and explore the research literature.Postgraduate students in economics with a good grasp of calculus, linear algebra, and probability and statistics will find themselves ready to tackle topics covered in this book. They will certainly benefit from the mathematical coverage in stochastic processes and stochastic differential equation with applications in finance. Postgraduate students in financial mathematics and financial engineering will also benefit, not only from the mathematical tools introduced in this book, but also from the economic ideas underpinning the economic modeling of financial markets.Both these groups of postgraduate students will learn the economic issues involved in financial modeling. The book can be used as an advanced text for Masters and PhD students in all subjects of financial economics, financial mathematics, mathematical finance, and financial engineering. It is also an ideal reference for practitioners and researchers in the subjects.
Download or read book Optimal Investment in Incomplete Markets with Multiple Brownian Externalities written by Levon Avanesyan and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An investor?s optimal market portfolio is shaped by their investment performance criterion. The latter is largely determined by the investor's idiosyncratic objectives and preferences. This dissertation contributes to the study of optimal investment under the expected utility of terminal wealth (Merton), as well as forward performance criteria. Our set-up is that of a continuous incomplete stock market model, where the incompleteness stems from multiple Brownian externalities. The externalities manifest themselves through the stock return and volatility coefficients, either explicitly by driving observable stochastic factors or implicitly by increasing the market filtration.In a Markovian multifactor market model we introduce the eigenvalue equality (EVE) stock-factor correlation structure, and construct a large class of forward performance processes (FPPs) with power-utility initial data, as well as their corresponding optimal portfolios. This is done by solving the associated non-linear parabolic partial differential equations (PDEs) posed in the ``wrong'' time direction. We establish on domains an explicit form of the generalized Widder's theorem of Nadtochiy and Tehranchi (Math. Financ. 27:438-470, 2015, Theorem 3.12) and rely hereby on the Laplace inversion in time of the solutions to suitable linear parabolic PDEs posed in the "right'' time direction.Next, we consider the Merton problem with power utility in a market model with the stock coefficients adapted to a factor-generated filtration. This setup admits market models with non-semimartingale factors. For models with EVE structure we find the optimal portfolio weights up to the computation of a certain conditional expectation, and explain how to evaluate the latter in affine Volterra factor models. We extend these results to a general stock-factor correlation setting for, what we will call, Sharpe ratio separable (SRS) market models.In our most general market model, we construct a broad class of FPPs with initial conditions of power mixture type, [mathematical formula omitted]. We derive the properties of two-power mixture FPPs when the risk aversion coefficients are continuous stochastic processes in (0,1), and provide a full characterization when the coefficients are constants. Finally, we discuss the problem of managing an investment pool of two investors, whose respective preferences evolve as power FPPs.
Download or read book An Introduction to Computational Finance written by mr U?ur and published by Imperial College Press. This book was released on 2009 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although there are several publications on similar subjects, this book mainly focuses on pricing of options and bridges the gap between Mathematical Finance and Numerical Methodologies. The author collects the key contributions of several monographs and selected literature, values and displays their importance, and composes them here to create a work which has its own characteristics in content and style.This invaluable book provides working Matlab codes not only to implement the algorithms presented in the text, but also to help readers code their own pricing algorithms in their preferred programming languages. Availability of the codes under an Internet site is also offered by the author.Not only does this book serve as a textbook in related undergraduate or graduate courses, but it can also be used by those who wish to implement or learn pricing algorithms by themselves. The basic methods of option pricing are presented in a self-contained and unified manner, and will hopefully help readers improve their mathematical and computational backgrounds for more advanced topics.Errata(s)Errata
