Mathematical Modeling In Economics And Finance Probability Stochastic Processes And Differential Equations

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Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations

Steven R. Dunbar
Mathematical Modeling in Economics and Finance Probability Stochastic Processes and Differential Equations Book PDF

Author : Steven R. Dunbar
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 41,7 Mb
Release : 2019-04-03
Category : Economics
ISBN : 9781470448394

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Mathematical Modeling in Economics and Finance: Probability, Stochastic Processes, and Differential Equations by Steven R. Dunbar Pdf

Mathematical Modeling in Economics and Finance is designed as a textbook for an upper-division course on modeling in the economic sciences. The emphasis throughout is on the modeling process including post-modeling analysis and criticism. It is a textbook on modeling that happens to focus on financial instruments for the management of economic risk. The book combines a study of mathematical modeling with exposure to the tools of probability theory, difference and differential equations, numerical simulation, data analysis, and mathematical analysis. Students taking a course from Mathematical Modeling in Economics and Finance will come to understand some basic stochastic processes and the solutions to stochastic differential equations. They will understand how to use those tools to model the management of financial risk. They will gain a deep appreciation for the modeling process and learn methods of testing and evaluation driven by data. The reader of this book will be successfully positioned for an entry-level position in the financial services industry or for beginning graduate study in finance, economics, or actuarial science. The exposition in Mathematical Modeling in Economics and Finance is crystal clear and very student-friendly. The many exercises are extremely well designed. Steven Dunbar is Professor Emeritus of Mathematics at the University of Nebraska and he has won both university-wide and MAA prizes for extraordinary teaching. Dunbar served as Director of the MAA's American Mathematics Competitions from 2004 until 2015. His ability to communicate mathematics is on full display in this approachable, innovative text.

Applied Stochastic Models and Control for Finance and Insurance

Charles S. Tapiero
Applied Stochastic Models and Control for Finance and Insurance Book PDF

Author : Charles S. Tapiero
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461558231

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Applied Stochastic Models and Control for Finance and Insurance by Charles S. Tapiero Pdf

Applied Stochastic Models and Control for Finance and Insurance presents at an introductory level some essential stochastic models applied in economics, finance and insurance. Markov chains, random walks, stochastic differential equations and other stochastic processes are used throughout the book and systematically applied to economic and financial applications. In addition, a dynamic programming framework is used to deal with some basic optimization problems. The book begins by introducing problems of economics, finance and insurance which involve time, uncertainty and risk. A number of cases are treated in detail, spanning risk management, volatility, memory, the time structure of preferences, interest rates and yields, etc. The second and third chapters provide an introduction to stochastic models and their application. Stochastic differential equations and stochastic calculus are presented in an intuitive manner, and numerous applications and exercises are used to facilitate their understanding and their use in Chapter 3. A number of other processes which are increasingly used in finance and insurance are introduced in Chapter 4. In the fifth chapter, ARCH and GARCH models are presented and their application to modeling volatility is emphasized. An outline of decision-making procedures is presented in Chapter 6. Furthermore, we also introduce the essentials of stochastic dynamic programming and control, and provide first steps for the student who seeks to apply these techniques. Finally, in Chapter 7, numerical techniques and approximations to stochastic processes are examined. This book can be used in business, economics, financial engineering and decision sciences schools for second year Master's students, as well as in a number of courses widely given in departments of statistics, systems and decision sciences.

Stochastic Methods in Economics and Finance

A.G. Malliaris
Stochastic Methods in Economics and Finance Book PDF

Author : A.G. Malliaris
Publisher : North Holland
Page : 332 pages
File Size : 45,8 Mb
Release : 1982
Category : Business & Economics
ISBN : UCSC:32106010712633

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Stochastic Methods in Economics and Finance by A.G. Malliaris Pdf

Theory and application of a variety of mathematical techniques in economics are presented in this volume. Topics discussed include: martingale methods, stochastic processes, optimal stopping, the modeling of uncertainty using a Wiener process, Itô's Lemma as a tool of stochastic calculus, and basic facts about stochastic differential equations. The notion of stochastic ability and the methods of stochastic control are discussed, and their use in economic theory and finance is illustrated with numerous applications. The applications covered include: futures, pricing, job search, stochastic capital theory, stochastic economic growth, the rational expectations hypothesis, a stochastic macroeconomic model, competitive firm under price uncertainty, the Black-Scholes option pricing theory, optimum consumption and portfolio rules, demand for index bonds, term structure of interest rates, the market risk adjustment in project valuation, demand for cash balances and an asset pricing model.

Measure, Probability, and Mathematical Finance

Guojun Gan,Chaoqun Ma,Hong Xie
Measure Probability and Mathematical Finance Book PDF

Author : Guojun Gan,Chaoqun Ma,Hong Xie
Publisher : John Wiley & Sons
Page : 54 pages
File Size : 45,8 Mb
Release : 2014-04-07
Category : Mathematics
ISBN : 9781118831960

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Measure, Probability, and Mathematical Finance by Guojun Gan,Chaoqun Ma,Hong Xie Pdf

An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.

Stochastic Control and Mathematical Modeling

Hiroaki Morimoto
Stochastic Control and Mathematical Modeling Book PDF

Author : Hiroaki Morimoto
Publisher : Cambridge University Press
Page : 340 pages
File Size : 51,9 Mb
Release : 2010-01-29
Category : Mathematics
ISBN : 0521195039

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Stochastic Control and Mathematical Modeling by Hiroaki Morimoto Pdf

This is a concise and elementary introduction to stochastic control and mathematical modeling. This book is designed for researchers in stochastic control theory studying its application in mathematical economics and those in economics who are interested in mathematical theory in control. It is also a good guide for graduate students studying applied mathematics, mathematical economics, and non-linear PDE theory. Contents include the basics of analysis and probability, the theory of stochastic differential equations, variational problems, problems in optimal consumption and in optimal stopping, optimal pollution control, and solving the HJB equation with boundary conditions. Major mathematical requisitions are contained in the preliminary chapters or in the appendix so that readers can proceed without referring to other materials.

Stochastic Processes and Calculus

Uwe Hassler
Stochastic Processes and Calculus Book PDF

Author : Uwe Hassler
Publisher : Springer
Page : 391 pages
File Size : 53,6 Mb
Release : 2015-12-12
Category : Business & Economics
ISBN : 9783319234281

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Stochastic Processes and Calculus by Uwe Hassler Pdf

This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus and processes have gained great importance, because they play a decisive role in the modeling of financial markets and as a basis for modern time series econometrics. Mathematical theory is applied to solve stochastic differential equations and to derive limiting results for statistical inference on nonstationary processes. This introduction is elementary and rigorous at the same time. On the one hand it gives a basic and illustrative presentation of the relevant topics without using many technical derivations. On the other hand many of the procedures are presented at a technically advanced level: for a thorough understanding, they are to be proven. In order to meet both requirements jointly, the present book is equipped with a lot of challenging problems at the end of each chapter as well as with the corresponding detailed solutions. Thus the virtual text - augmented with more than 60 basic examples and 40 illustrative figures - is rather easy to read while a part of the technical arguments is transferred to the exercise problems and their solutions.

The Mathematics of Financial Modeling and Investment Management

Sergio M. Focardi,Frank J. Fabozzi, CFA
The Mathematics of Financial Modeling and Investment Management Book PDF

Author : Sergio M. Focardi,Frank J. Fabozzi, CFA
Publisher : John Wiley & Sons
Page : 804 pages
File Size : 45,5 Mb
Release : 2004-03-29
Category : Business & Economics
ISBN : 0471465992

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The Mathematics of Financial Modeling and Investment Management by Sergio M. Focardi,Frank J. Fabozzi, CFA Pdf

the mathematics of financial modeling & investment management The Mathematics of Financial Modeling & Investment Management covers a wide range of technical topics in mathematics and finance-enabling the investment management practitioner, researcher, or student to fully understand the process of financial decision-making and its economic foundations. This comprehensive resource will introduce you to key mathematical techniques-matrix algebra, calculus, ordinary differential equations, probability theory, stochastic calculus, time series analysis, optimization-as well as show you how these techniques are successfully implemented in the world of modern finance. Special emphasis is placed on the new mathematical tools that allow a deeper understanding of financial econometrics and financial economics. Recent advances in financial econometrics, such as tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are discussed in depth. Using a wealth of real-world examples, Focardi and Fabozzi simultaneously show both the mathematical techniques and the areas in finance where these techniques are applied. They also cover a variety of useful financial applications, such as: * Arbitrage pricing * Interest rate modeling * Derivative pricing * Credit risk modeling * Equity and bond portfolio management * Risk management * And much more Filled with in-depth insight and expert advice, The Mathematics of Financial Modeling & Investment Management clearly ties together financial theory and mathematical techniques.

Simulation and Inference for Stochastic Differential Equations

Stefano M. Iacus
Simulation and Inference for Stochastic Differential Equations Book PDF

Author : Stefano M. Iacus
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 53,8 Mb
Release : 2009-04-27
Category : Computers
ISBN : 9780387758398

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Simulation and Inference for Stochastic Differential Equations by Stefano M. Iacus Pdf

This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too.

Stochastic Economic Dynamics

Bjarne S. Jensen,Tapio Palokangas
Stochastic Economic Dynamics Book PDF

Author : Bjarne S. Jensen,Tapio Palokangas
Publisher : Copenhagen Business School Press DK
Page : 464 pages
File Size : 41,8 Mb
Release : 2007
Category : Business & Economics
ISBN : 8763001853

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Stochastic Economic Dynamics by Bjarne S. Jensen,Tapio Palokangas Pdf

This book analyzes stochastic dynamic systems across a broad spectrum in economics and finance. The major unifying theme is the coherent and rigorous treatment of uncertainty and its implications for describing stochastic processes by the stochastic differential equations of the fundamental models in various fields. Pertinent subjects are interrelated, juxtaposed, and examined for consistency in theoretical and empirical contexts. The volume consists of three parts: Developments in Stochastic Dynamics; Stochastic Dynamics in Basic Economic Growth Models; and Intertemporal Optimization in Consumption, Finance, and Growth. Key topics include: fractional Brownian motion in finance; moment evolution of Gaussian and geometric Wiener diffusions; stochastic kinematics and stochastic mechanics; stochastic growth in continuous time; time delays and Hopf bifurcation; consumption and investment strategies; differential systems in finance and life insurance; uncertainty of technological innovations; investment and employment cycles; stochastic control theory; and risk aversion. The works collected in this book serves to bridge the "old" deterministic dynamics and the "new" stochastic dynamics. The collection is important for scholars and advanced graduate students of economics, statistics, and applied mathematics.

Stochastic Modeling in Economics and Finance

Jitka Dupacova,J. Hurt,J. Stepan
Stochastic Modeling in Economics and Finance Book PDF

Author : Jitka Dupacova,J. Hurt,J. Stepan
Publisher : Springer
Page : 386 pages
File Size : 43,9 Mb
Release : 2010-12-07
Category : Mathematics
ISBN : 1441952314

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Stochastic Modeling in Economics and Finance by Jitka Dupacova,J. Hurt,J. Stepan Pdf

In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities. Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects. Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study.

An Introduction to Continuous-Time Stochastic Processes

Vincenzo Capasso,David Bakstein
An Introduction to Continuous Time Stochastic Processes Book PDF

Author : Vincenzo Capasso,David Bakstein
Publisher : Birkhäuser
Page : 560 pages
File Size : 55,7 Mb
Release : 2022-06-20
Category : Mathematics
ISBN : 3030696553

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An Introduction to Continuous-Time Stochastic Processes by Vincenzo Capasso,David Bakstein Pdf

This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.

Parameter Estimation in Stochastic Differential Equations

Jaya P. N. Bishwal
Parameter Estimation in Stochastic Differential Equations Book PDF

Author : Jaya P. N. Bishwal
Publisher : Springer
Page : 268 pages
File Size : 45,6 Mb
Release : 2007-09-26
Category : Mathematics
ISBN : 9783540744481

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Parameter Estimation in Stochastic Differential Equations by Jaya P. N. Bishwal Pdf

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Mathematical Models in Finance

S.D. Howison,F.P. Kelly,P. Wilmott
Mathematical Models in Finance Book PDF

Author : S.D. Howison,F.P. Kelly,P. Wilmott
Publisher : CRC Press
Page : 164 pages
File Size : 53,5 Mb
Release : 1995-05-15
Category : Mathematics
ISBN : 0412630702

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Mathematical Models in Finance by S.D. Howison,F.P. Kelly,P. Wilmott Pdf

Mathematical Models in Finance compiles papers presented at the Royal Society of London discussion meeting. Topics range from the foundations of classical theory to sophisticated, up-to-date mathematical modeling and analysis. In the wake of the increased level of mathematical awareness in the financial research community, attention has focused on fundamental issues of market modelling that are not adequately allowed for in the standard analyses. Examples include market anomalies and nonlinear coupling effects, and demand new synthesis of mathematical and numerical techniques. This line of inquiry is further stimulated by ever tightening profits due to increased competition. Several papers in this volume offer pointers to future developments in this area.

Modern Stochastics and Applications

Volodymyr Korolyuk,Nikolaos Limnios,Yuliya Mishura,Lyudmyla Sakhno,Georgiy Shevchenko
Modern Stochastics and Applications Book PDF

Author : Volodymyr Korolyuk,Nikolaos Limnios,Yuliya Mishura,Lyudmyla Sakhno,Georgiy Shevchenko
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 51,6 Mb
Release : 2014-01-30
Category : Mathematics
ISBN : 9783319035123

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Modern Stochastics and Applications by Volodymyr Korolyuk,Nikolaos Limnios,Yuliya Mishura,Lyudmyla Sakhno,Georgiy Shevchenko Pdf

This volume presents an extensive overview of all major modern trends in applications of probability and stochastic analysis. It will be a great source of inspiration for designing new algorithms, modeling procedures and experiments. Accessible to researchers, practitioners, as well as graduate and postgraduate students, this volume presents a variety of new tools, ideas and methodologies in the fields of optimization, physics, finance, probability, hydrodynamics, reliability, decision making, mathematical finance, mathematical physics and economics. Contributions to this Work include those of selected speakers from the international conference entitled “Modern Stochastics: Theory and Applications III,” held on September 10 –14, 2012 at Taras Shevchenko National University of Kyiv, Ukraine. The conference covered the following areas of research in probability theory and its applications: stochastic analysis, stochastic processes and fields, random matrices, optimization methods in probability, stochastic models of evolution systems, financial mathematics, risk processes and actuarial mathematics and information security.

Modeling with Itô Stochastic Differential Equations

E. Allen
Modeling with It Stochastic Differential Equations Book PDF

Author : E. Allen
Publisher : Springer
Page : 0 pages
File Size : 40,7 Mb
Release : 2007-03-09
Category : Mathematics
ISBN : 1402059523

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Modeling with Itô Stochastic Differential Equations by E. Allen Pdf

This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.