Functionally Generated Portfolios In Stochastic Portfolio Theory
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Functionally Generated Portfolios In Stochastic Portfolio Theory
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Author : Kangjianan Xie
language : en
Publisher:
Release Date : 2020
Functionally Generated Portfolios In Stochastic Portfolio Theory written by Kangjianan Xie and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
In this dissertation, we focus on constructing trading strategies through the method of functional generation. Such a construction is of great importance in Stochastic Portfolio Theory established by Robert Fernholz. This method is simplified by Karatzas and Ruf (Finance and Stochastics 21.3:753-787, 2017), where they also propose another method called additive functional generation. Inspired by their work, we first investigate the dependence of functional generation on an extra finite-variation process. A mollification argument and Komlós theorem yield a general class of potential arbitrage strategies. Secondly, we extend the analysis by incorporating transaction costs proportional to the trading volume. The performance of several portfolios in the presence of dividends and transaction costs is examined under different configurations. Next, we analyse the so-called leakage effect used to measure the loss in portfolio wealth due to renewing the portfolio constituents. Moreover, we further explore the method of additive functional generation by considering the conjugate of a portfolio generating function. The connection between functional generation and optimal transport is also studied. An extended abstract can be found before the first chapter of this dissertation.
Stochastic Portfolio Theory
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Author : E. Robert Fernholz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Stochastic Portfolio Theory written by E. Robert Fernholz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Business & Economics categories.
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. On a practical level, stochastic portfolio theory has been the basis for strategies used for over a decade by the institutional equity manager INTECH, where the author has served as chief investment officer. 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.
Quantitative Analysis In Financial Markets Collected Papers Of The New York University Mathematical Finance Seminar
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Author : Marco Avellaneda
language : en
Publisher: World Scientific
Release Date : 1999-10-27
Quantitative Analysis In Financial Markets Collected Papers Of The New York University Mathematical Finance Seminar written by Marco Avellaneda and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-27 with Business & Economics categories.
This invaluable book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modeling. Most are faculty members at leading universities or Wall Street practitioners.The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Specific articles concern topics such as option theory, dynamic hedging, interest-rate modeling, portfolio theory, price forecasting using statistical methods, etc.
Generalizations Of Functionally Generated Portfolios With Applications To Statistical Arbitrage
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Author : Winslow Strong
language : en
Publisher:
Release Date : 2013
Generalizations Of Functionally Generated Portfolios With Applications To Statistical Arbitrage written by Winslow Strong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the numéraire. This description has proven to be analytically very useful, as it is both pathwise and free of stochastic integrals. Here we generalize the class of FGPs in several ways: (1) the numéraire may be any strictly positive wealth process, not necessarily the market portfolio or even a passive portfolio; (2) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation. These generalizations do not forfeit the important tractability properties of the associated master equation. We show how these generalizations can be usefully applied to scenario analysis, statistical arbitrage, portfolio risk immunization, and the theory of mirror portfolios.
Portfolio Theory And Arbitrage A Course In Mathematical Finance
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Author : Ioannis Karatzas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-20
Portfolio Theory And Arbitrage A Course In Mathematical Finance written by Ioannis Karatzas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Education categories.
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.
Geometric Structures Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer
Release Date : 2018-11-19
Geometric Structures Of Information written by Frank Nielsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-19 with Technology & Engineering categories.
This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.
Arbitrage And Stochastic Portfolio Theory In Stochastic Dimension
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Author : Winslow Carter Strong
language : en
Publisher:
Release Date : 2011
Arbitrage And Stochastic Portfolio Theory In Stochastic Dimension written by Winslow Carter Strong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
The topic motivating this dissertation is functionally generated portfolios and their capacity to deliver relative arbitrage, an aspect of stochastic portfolio theory (SPT). The aim is to relax some of the common assumptions of SPT and explore the performance of functionally generated portfolios in this more general setting, with an eye towards arbitrage. In particular, the assumption of a constant number of companies in the market model is relaxed, as well as the assumption that all changes in capitalizations are passed on as returns to investors through the stochastic integral.
Topics In Stochastic Portfolio Theory
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Author : Donghan Kim
language : en
Publisher:
Release Date : 2020
Topics In Stochastic Portfolio Theory written by Donghan Kim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
The second part develops portfolio theory in open markets. An open market is a subset of the entire equity market, composed of a certain fixed number of top-capitalization stocks. Though the number of stocks in open market is fixed, the constituents of the market change over time as each company's rank by its market capitalization fluctuates. When one is allowed to invest also in money market, an open market resembles the entire 'closed' equity market in the sense that most of the results that are valid for the entire market, continue to hold when investment is restricted to the open market. One of these results is the equivalence of market viability (lack of arbitrage) and the existence of num\'eraire portfolio (portfolio which cannot be outperformed). When access to the money market is prohibited, the class of portfolios shrinks significantly in open markets. In such a case, we discuss the Capital Asset Pricing Model, how to construct functionally-generated portfolios, and the concept of universal portfolio in open market setting.
The Handbook Of World Stock Derivative Commodity Exchanges
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Author :
language : en
Publisher:
Release Date : 2001
The Handbook Of World Stock Derivative Commodity Exchanges written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Commodity exchanges categories.
Measurement Of Productivity And Efficiency
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Author : Robin C. Sickles
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-28
Measurement Of Productivity And Efficiency written by Robin C. Sickles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-28 with Business & Economics categories.
Provides a comprehensive approach to productivity and efficiency analysis using economic and econometric theory.