Stochastic Portfolio Theory

Author: E. Robert Fernholz

Publisher: Springer Science & Business Media

ISBN: 1475736991

Category: Business & Economics

Page: 178

View: 9630

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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.
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Mathematical Modelling and Numerical Methods in Finance

Special Volume

Author: N.A

Publisher: Elsevier

ISBN: 0080931006

Category: Mathematics

Page: 684

View: 8924

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Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field
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Stochastic Control of Hereditary Systems and Applications

Author: Mou-Hsiung Chang

Publisher: Springer Science & Business Media

ISBN: 9780387758169

Category: Mathematics

Page: 406

View: 5995

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This monograph develops the Hamilton-Jacobi-Bellman theory via dynamic programming principle for a class of optimal control problems for stochastic hereditary differential equations (SHDEs) driven by a standard Brownian motion and with a bounded or an infinite but fading memory. These equations represent a class of stochastic infinite-dimensional systems that become increasingly important and have wide range of applications in physics, chemistry, biology, engineering and economics/finance. This monograph can be used as a reference for those who have special interest in optimal control theory and applications of stochastic hereditary systems.
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Stochastic Calculus and Financial Applications

Author: J. Michael Steele

Publisher: Springer Science & Business Media

ISBN: 1468493051

Category: Mathematics

Page: 302

View: 1519

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Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH
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Stochastic Integration and Differential Equations

Author: Philip Protter

Publisher: Springer

ISBN: 3662100614

Category: Mathematics

Page: 415

View: 4999

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It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though it is no longer appropriate to call it "a new approach". The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises. Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chapter 3 has been completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chapter 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery’s examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, a treatment of the Fefferman martingale inequality, and that the dual space of the martingale space H^1 can be identified with BMO martingales. Solutions to selected exercises are available at the web site of the author, with current URL http://www.orie.cornell.edu/~protter/books.html.
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Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6814

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Controlled Markov Processes and Viscosity Solutions

Author: Wendell H. Fleming,Halil Mete Soner

Publisher: Springer Science & Business Media

ISBN: 0387310711

Category: Mathematics

Page: 429

View: 9733

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This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
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Advances in Mathematical Economics

Author: S. Kusuoka,A. Yamazaki

Publisher: Springer

ISBN: N.A

Category: Business & Economics

Page: 130

View: 4942

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A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.
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Stochastic Calculus with Applications to Stochastic Portfolio Optimisation

Author: Daniel Michelbrink

Publisher: diplom.de

ISBN: 3836612879

Category: Mathematics

Page: 96

View: 1566

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Inhaltsangabe:Introduction: The present paper is about continuous time stochastic calculus and its application to stochastic portfolio selection problems. The paper is divided into two parts: The first part provides the mathematical framework and consists of Chapters 1 and 2, where it gives an insight into the theory of stochastic process and the theory of stochastic calculus. The second part, consisting of Chapters 3 and 4, applies the first part to problems in stochastic portfolio theory and stochastic portfolio optimisation. Chapter 1, "Stochastic Processes", starts with the construction of stochastic process. The significance of Markovian kernels is discussed and some examples of process and emigroups will be given. The simple normal-distribution will be extended to the multi-variate normal distribution, which is needed for introducing the Brownian motion process. Finally, another class of stochastic process is introduced which plays a central role in mathematical finance: the martingale. Chapter 2, "Stochastic Calculus", begins with the introduction of the stochastic integral. This integral is different to the Lebesgue-Stieltjes integral because of the randomness of the integrand and integrator. This is followed by the probably most important theorem in stochastic calculus: It o s formula. It o s formula is of central importance and most of the proofs of Chapters 3 and 4 are not possible without it. We continue with the notion of a stochastic differential equations. We introduce strong and weak solutions and a way to solve stochastic differential equations by removing the drift. The last section of Chapter 2 applies stochastic calculus to stochastic control. We will need stochastic control to solve some portfolio problems in Chapter 4. Chapter 3, "Stochastic Portfolio Theory", deals mainly with the problem of introducing an appropriate model for stock prices and portfolios. These models will be needed in Chapter 4. The first section of Chapter 3 introduces a stock market model, portfolios, the risk-less asset, consumption and labour income processes. The second section, Section 3.2, introduces the notion of relative return as well as portfolio generating functions. Relative return finds application in Chapter 4 where we deal with benchmark optimisation. Benchmark optimisation is optimising a portfolio with respect to a given benchmark portfolio. The final section of Chapter 3 contains some considerations about the long-term behaviour of [...]
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