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Stochastic Portfolio Theory

Author: E. Robert Fernholz
Publisher: Springer Science & Business Media
ISBN: 1475736991
Size: 34.80 MB
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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.

Stochastic Control Of Hereditary Systems And Applications

Author: Mou-Hsiung Chang
Publisher: Springer Science & Business Media
ISBN: 9780387758169
Size: 30.68 MB
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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.

Mathematical Modelling And Numerical Methods In Finance

Author:
Publisher: Elsevier
ISBN: 0080931006
Size: 15.36 MB
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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

Stochastic Integration And Differential Equations

Author: Philip Protter
Publisher: Springer
ISBN: 3662100614
Size: 77.94 MB
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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.

Stochastic Calculus With Applications To Stochastic Portfolio Optimisation

Author: Daniel Michelbrink
Publisher: diplom.de
ISBN: 3836612879
Size: 44.34 MB
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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 [...]

Stochastic Calculus And Financial Applications

Author: J. Michael Steele
Publisher: Springer Science & Business Media
ISBN: 1468493051
Size: 28.61 MB
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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

Continuous Time Stochastic Control And Optimization With Financial Applications

Author: Huyên Pham
Publisher: Springer Science & Business Media
ISBN: 3540895000
Size: 47.44 MB
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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.

Semi Markov Models And Applications

Author: Jacques Janssen
Publisher: Springer Science & Business Media
ISBN: 1461332885
Size: 42.44 MB
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This book presents a selection of papers presented to the Second Inter national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Brussels in 1984 : to make, fourteen years later, the state of the art in the field of semi-Markov processes and their applications, bring together researchers in this field and also to stimulate fruitful discussions. The set of the subjects of the papers presented in Compiegne has a lot of similarities with the preceding Symposium; this shows that the main fields of semi-Markov processes are now well established particularly for basic applications in Reliability and Maintenance, Biomedicine, Queue ing, Control processes and production. A growing field is the one of insurance and finance but this is not really a surprising fact as the problem of pricing derivative products represents now a crucial problem in economics and finance. For example, stochastic models can be applied to financial and insur ance models as we have to evaluate the uncertainty of the future market behavior in order, firstly, to propose different measures for important risks such as the interest risk, the risk of default or the risk of catas trophe and secondly, to describe how to act in order to optimize the situation in time. Recently, the concept of VaR (Value at Risk) was "discovered" in portfolio theory enlarging so the fundamental model of Markowitz.

Monte Carlo Methods In Financial Engineering

Author: Paul Glasserman
Publisher: Springer Science & Business Media
ISBN: 0387216170
Size: 25.94 MB
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From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis