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Random Dynamical Systems in Finance

Random Dynamical Systems in Finance
Author: Anatoliy Swishchuk
Publisher: CRC Press
Total Pages: 354
Release: 2016-04-19
Genre: Business & Economics
ISBN: 1439867194

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The theory and applications of random dynamical systems (RDS) are at the cutting edge of research in mathematics and economics, particularly in modeling the long-run evolution of economic systems subject to exogenous random shocks. Despite this interest, there are no books available that solely focus on RDS in finance and economics. Exploring this


Random Dynamical Systems

Random Dynamical Systems
Author: Rabi Bhattacharya
Publisher: Cambridge University Press
Total Pages: 5
Release: 2007-01-08
Genre: Mathematics
ISBN: 1139461621

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This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.


Topological Dynamics of Random Dynamical Systems

Topological Dynamics of Random Dynamical Systems
Author: Nguyen Dinh Cong
Publisher: Oxford University Press
Total Pages: 216
Release: 1997
Genre: Mathematics
ISBN: 9780198501572

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This book is the first systematic treatment of the theory of topological dynamics of random dynamical systems. A relatively new field, the theory of random dynamical systems unites and develops the classical deterministic theory of dynamical systems and probability theory, finding numerous applications in disciplines ranging from physics and biology to engineering, finance and economics. This book presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structural stability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory.


Dynamic Systems and Control Engineering

Dynamic Systems and Control Engineering
Author: Nader Jalili
Publisher: Cambridge University Press
Total Pages: 948
Release: 2023-05-31
Genre: Technology & Engineering
ISBN: 1108912923

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Using a step-by-step approach, this textbook provides a modern treatment of the fundamental concepts, analytical techniques, and software tools used to perform multi-domain modeling, system analysis and simulation, linear control system design and implementation, and advanced control engineering. Chapters follow a progressive structure, which builds from modeling fundamentals to analysis and advanced control while showing the interconnections between topics, and solved problems and examples are included throughout. Students can easily recall key topics and test understanding using Review Note and Concept Quiz boxes, and over 200 end-of-chapter homework exercises with accompanying Concept Keys are included. Focusing on practical understanding, students will gain hands-on experience of many modern MATLAB® tools, including Simulink® and physical modeling in SimscapeTM. With a solutions manual, MATLAB® code, and Simulink®/SimscapeTM files available online, this is ideal for senior undergraduates taking courses on modeling, analysis and control of dynamic systems, as well as graduates studying control engineering.


Handbook of Financial Markets: Dynamics and Evolution

Handbook of Financial Markets: Dynamics and Evolution
Author: Thorsten Hens
Publisher: Elsevier
Total Pages: 607
Release: 2009-06-12
Genre: Business & Economics
ISBN: 0080921434

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The models of portfolio selection and asset price dynamics in this volume seek to explain the market dynamics of asset prices. Presenting a range of analytical, empirical, and numerical techniques as well as several different modeling approaches, the authors depict the state of debate on the market selection hypothesis. By explicitly assuming the heterogeneity of investors, they present models that are descriptive and normative as well, making the volume useful for both finance theorists and financial practitioners. Explains the market dynamics of asset prices, offering insights about asset management approaches Assumes a heterogeneity of investors that yields descriptive and normative models of portfolio selections and asset pricing dynamics


Dynamical Systems with Applications Using Mathematica®

Dynamical Systems with Applications Using Mathematica®
Author: Stephen Lynch
Publisher: Birkhäuser
Total Pages: 585
Release: 2017-10-12
Genre: Mathematics
ISBN: 3319614851

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This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.


Mathematical and Statistical Methods for Insurance and Finance

Mathematical and Statistical Methods for Insurance and Finance
Author: Cira Perna
Publisher: Springer Science & Business Media
Total Pages: 212
Release: 2007-12-12
Genre: Business & Economics
ISBN: 8847007046

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The interaction between mathematicians and statisticians reveals to be an effective approach to the analysis of insurance and financial problems, in particular in an operative perspective. The Maf2006 conference, held at the University of Salerno in 2006, had precisely this purpose and the collection published here gathers some of the papers presented at the conference and successively worked out to this aim. They cover a wide variety of subjects in insurance and financial fields.


Applied Nonautonomous and Random Dynamical Systems

Applied Nonautonomous and Random Dynamical Systems
Author: Tomás Caraballo
Publisher: Springer
Total Pages: 108
Release: 2017-01-31
Genre: Mathematics
ISBN: 3319492470

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This book offers an introduction to the theory of non-autonomous and stochastic dynamical systems, with a focus on the importance of the theory in the Applied Sciences. It starts by discussing the basic concepts from the theory of autonomous dynamical systems, which are easier to understand and can be used as the motivation for the non-autonomous and stochastic situations. The book subsequently establishes a framework for non-autonomous dynamical systems, and in particular describes the various approaches currently available for analysing the long-term behaviour of non-autonomous problems. Here, the major focus is on the novel theory of pullback attractors, which is still under development. In turn, the third part represents the main body of the book, introducing the theory of random dynamical systems and random attractors and revealing how it may be a suitable candidate for handling realistic models with stochasticity. A discussion of future research directions serves to round out the coverage.


Financial Economics

Financial Economics
Author: Thorsten Hens
Publisher: Springer Science & Business Media
Total Pages: 377
Release: 2010-07-01
Genre: Business & Economics
ISBN: 3540361480

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Financial economics is a fascinating topic where ideas from economics, mathematics and, most recently, psychology are combined to understand financial markets. This book gives a concise introduction into this field and includes for the first time recent results from behavioral finance that help to understand many puzzles in traditional finance. The book is tailor made for master and PhD students and includes tests and exercises that enable the students to keep track of their progress. Parts of the book can also be used on a bachelor level. Researchers will find it particularly useful as a source for recent results in behavioral finance and decision theory.


Global Analysis of Dynamic Models in Economics and Finance

Global Analysis of Dynamic Models in Economics and Finance
Author: Gian Italo Bischi
Publisher: Springer Science & Business Media
Total Pages: 449
Release: 2012-08-07
Genre: Business & Economics
ISBN: 3642295037

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The essays in this special volume survey some of the most recent advances in the global analysis of dynamic models for economics, finance and the social sciences. They deal in particular with a range of topics from mathematical methods as well as numerous applications including recent developments on asset pricing, heterogeneous beliefs, global bifurcations in complementarity games, international subsidy games and issues in economic geography. A number of stochastic dynamic models are also analysed. The book is a collection of essays in honour of the 60th birthday of Laura Gardini.​