## Stochastic Portfolio Theory

Author: E. Robert Fernholz

Publisher: Springer Science & Business Media

ISBN: 1475736991

Page: 178

View: 504

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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## Stochastic Calculus with Applications to Stochastic Portfolio Optimisation

Author: Daniel Michelbrink

Publisher: diplom.de

ISBN: 3836612879

Category: Mathematics

Page: 96

View: 4914

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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## Stochastic Control of Hereditary Systems and Applications

Author: Mou-Hsiung Chang

Publisher: Springer Science & Business Media

ISBN: 9780387758169

Category: Mathematics

Page: 406

View: 982

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: 6881

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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## Mathematical Finance

Deterministic and Stochastic Models

Author: Jacques Janssen,Raimondo Manca,Ernesto Volpe

Publisher: John Wiley & Sons

ISBN: 1118622413

Category: Mathematics

Page: 720

View: 2825

This book provides a detailed study of Financial Mathematics. In addition to the extraordinary depth the book provides, it offers a study of the axiomatic approach that is ideally suited for analyzing financial problems. This book is addressed to MBA's, Financial Engineers, Applied Mathematicians, Banks, Insurance Companies, and Students of Business School, of Economics, of Applied Mathematics, of Financial Engineering, Banks, and more.
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## Applied Probability and Queues

Author: Soeren Asmussen,Søren Asmussen

Publisher: Springer Science & Business Media

ISBN: 9780387002118

Page: 438

View: 8811

This updated new edition introduces the reader to the fundamentals of queueing theory, including Markov processes and random walks. It contains an extended treatment of queueing networks and matrix analytic methods as well as additional topics like Poisson's equation, Palm theory and heavy tails.
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Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1551

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Author: S. Kusuoka,A. Yamazaki

Publisher: Springer

ISBN: N.A

Page: 130

View: 7480

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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## Option Pricing and Portfolio Optimization

Modern Methods of Financial Mathematics

Author: Ralf Korn,Elke Korn

Publisher: American Mathematical Soc.

ISBN: 9780821821237

Category: Mathematics

Page: 253

View: 746