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Stochastic Models of Financial Mathematics

Stochastic Models of Financial Mathematics
A Book

by Vigirdas Mackevicius

  • Publisher : Elsevier
  • Release : 2016-11-08
  • Pages : 130
  • ISBN : 0081020864
  • Language : En, Es, Fr & De
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This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black-Scholes and interest rate models. Other topics covered include self-financing strategies, option pricing, exotic options and risk-neutral probabilities. Vasicek, Cox-Ingersoll-Ross, and Heath-Jarrow-Morton interest rate models are also explored. The author presents practitioners with a basic introduction, with more rigorous information provided for mathematicians. The reader is assumed to be familiar with the basics of probability theory. Some basic knowledge of stochastic integration and differential equations theory is preferable, although all preliminary information is given in the first part of the book. Some relatively simple theoretical exercises are also provided. About continuous-time stochastic models of financial mathematics Black-Sholes model and interest rate models Requiring a minimum knowledge of stochastic integration and stochastic differential equations

Mathematical Finance

Mathematical Finance
Deterministic and Stochastic Models

by Jacques Janssen,Raimondo Manca,Ernesto Volpe

  • Publisher : John Wiley & Sons
  • Release : 2013-03-07
  • Pages : 720
  • ISBN : 1118622413
  • Language : En, Es, Fr & De
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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.

Exam Prep for: Stochastic Models of Financial Mathematics

Exam Prep for: Stochastic Models of Financial Mathematics
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2021
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Stochastic Financial Models

Stochastic Financial Models
A Book

by Douglas Kennedy

  • Publisher : CRC Press
  • Release : 2016-04-19
  • Pages : 264
  • ISBN : 1439882711
  • Language : En, Es, Fr & De
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Filling the void between surveys of the field with relatively light mathematical content and books with a rigorous, formal approach to stochastic integration and probabilistic ideas, Stochastic Financial Models provides a sound introduction to mathematical finance. The author takes a classical applied mathematical approach, focusing on calculations rather than seeking the greatest generality. Developed from the esteemed author’s advanced undergraduate and graduate courses at the University of Cambridge, the text begins with the classical topics of utility and the mean-variance approach to portfolio choice. The remainder of the book deals with derivative pricing. The author fully explains the binomial model since it is central to understanding the pricing of derivatives by self-financing hedging portfolios. He then discusses the general discrete-time model, Brownian motion and the Black–Scholes model. The book concludes with a look at various interest-rate models. Concepts from measure-theoretic probability and solutions to the end-of-chapter exercises are provided in the appendices. By exploring the important and exciting application area of mathematical finance, this text encourages students to learn more about probability, martingales and stochastic integration. It shows how mathematical concepts, such as the Black–Scholes and Gaussian random-field models, are used in financial situations.

Stochastic Modeling in Economics and Finance

Stochastic Modeling in Economics and Finance
A Book

by Jitka Dupacova,J. Hurt,J. Stepan

  • Publisher : Springer Science & Business Media
  • Release : 2006-04-18
  • Pages : 386
  • ISBN : 0306481677
  • Language : En, Es, Fr & De
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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.

Essentials of Stochastic Finance

Essentials of Stochastic Finance
Facts, Models, Theory

by Albert N. Shiryaev

  • Publisher : World Scientific
  • Release : 1999
  • Pages : 834
  • ISBN : 9810236050
  • Language : En, Es, Fr & De
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Readership: Undergraduates and researchers in probability and statistics; applied, pure and financial mathematics; economics; chaos.

Mathematical Finance 2

Mathematical Finance 2
Stochastic Models

by Jacques Janssen,Raimondo Manca,Ernesto Volpe

  • Publisher : Iste/Hermes Science Pub
  • Release : 2008-01
  • Pages : 352
  • ISBN : 9781905209859
  • Language : En, Es, Fr & De
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This succinct overview examines stochastic processes and Itô’s formula, the main tool of stochastic finance. Classical fields—such as the evaluation of equity options, the basis of quantitative risk management, and interest rate stochastic models and how they are applied to bond options—are also discussed along with the increasingly important areas of Markov and semi-Markov risk and evaluation models.

Stochastic Finance

Stochastic Finance
An Introduction in Discrete Time

by Hans Föllmer,Alexander Schied

  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 2016-07-25
  • Pages : 608
  • ISBN : 3110463458
  • Language : En, Es, Fr & De
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This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This fourth, newly revised edition contains more than one hundred exercises. It also includes material on risk measures and the related issue of model uncertainty, in particular a chapter on dynamic risk measures and sections on robust utility maximization and on efficient hedging with convex risk measures. Contents: Part I: Mathematical finance in one period Arbitrage theory Preferences Optimality and equilibrium Monetary measures of risk Part II: Dynamic hedging Dynamic arbitrage theory American contingent claims Superhedging Efficient hedging Hedging under constraints Minimizing the hedging error Dynamic risk measures

Stochastic Finance

Stochastic Finance
An Introduction with Market Examples

by Nicolas Privault

  • Publisher : CRC Press
  • Release : 2013-12-20
  • Pages : 441
  • ISBN : 1466594020
  • Language : En, Es, Fr & De
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Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of finance and stochastic calculus, and builds up to special topics, such as options, derivatives, and credit default and jump processes. It details the techniques required to model the time evolution of risky assets. The book discusses a wide range of classical topics including Black–Scholes pricing, exotic and American options, term structure modeling and change of numéraire, as well as models with jumps. The author takes the approach adopted by mainstream mathematical finance in which the computation of fair prices is based on the absence of arbitrage hypothesis, therefore excluding riskless profit based on arbitrage opportunities and basic (buying low/selling high) trading. With 104 figures and simulations, along with about 20 examples based on actual market data, the book is targeted at the advanced undergraduate and graduate level, either as a course text or for self-study, in applied mathematics, financial engineering, and economics.

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

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

by Steven R. Dunbar

  • Publisher : American Mathematical Soc.
  • Release : 2019-04-03
  • Pages : 232
  • ISBN : 1470448394
  • Language : En, Es, Fr & De
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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.

Introduction to Stochastic Finance

Introduction to Stochastic Finance
A Book

by Jia-An Yan

  • Publisher : Springer
  • Release : 2018-10-10
  • Pages : 403
  • ISBN : 9811316570
  • Language : En, Es, Fr & De
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This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems. The general theory of static risk measures, basic concepts and results on markets of semimartingale model, and a numeraire-free and original probability based framework for financial markets are also included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary knowledge, are presented.

Methods of Mathematical Finance

Methods of Mathematical Finance
A Book

by Ioannis Karatzas,Steven Shreve

  • Publisher : Springer
  • Release : 2017-01-10
  • Pages : 415
  • ISBN : 1493968459
  • Language : En, Es, Fr & De
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This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

Stochastic Processes with Applications to Finance

Stochastic Processes with Applications to Finance
A Book

by Masaaki Kijima

  • Publisher : CRC Press
  • Release : 2016-04-19
  • Pages : 343
  • ISBN : 1439884846
  • Language : En, Es, Fr & De
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Financial engineering has been proven to be a useful tool for risk management, but using the theory in practice requires a thorough understanding of the risks and ethical standards involved. Stochastic Processes with Applications to Finance, Second Edition presents the mathematical theory of financial engineering using only basic mathematical tools

Financial Modeling

Financial Modeling
A Backward Stochastic Differential Equations Perspective

by Stephane Crepey

  • Publisher : Springer Science & Business Media
  • Release : 2013-06-13
  • Pages : 459
  • ISBN : 3642371132
  • Language : En, Es, Fr & De
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Backward stochastic differential equations (BSDEs) provide a general mathematical framework for solving pricing and risk management questions of financial derivatives. They are of growing importance for nonlinear pricing problems such as CVA computations that have been developed since the crisis. Although BSDEs are well known to academics, they are less familiar to practitioners in the financial industry. In order to fill this gap, this book revisits financial modeling and computational finance from a BSDE perspective, presenting a unified view of the pricing and hedging theory across all asset classes. It also contains a review of quantitative finance tools, including Fourier techniques, Monte Carlo methods, finite differences and model calibration schemes. With a view to use in graduate courses in computational finance and financial modeling, corrected problem sets and Matlab sheets have been provided. Stéphane Crépey’s book starts with a few chapters on classical stochastic processes material, and then... fasten your seatbelt... the author starts traveling backwards in time through backward stochastic differential equations (BSDEs). This does not mean that one has to read the book backwards, like a manga! Rather, the possibility to move backwards in time, even if from a variety of final scenarios following a probability law, opens a multitude of possibilities for all those pricing problems whose solution is not a straightforward expectation. For example, this allows for framing problems like pricing with credit and funding costs in a rigorous mathematical setup. This is, as far as I know, the first book written for several levels of audiences, with applications to financial modeling and using BSDEs as one of the main tools, and as the song says: "it's never as good as the first time". Damiano Brigo, Chair of Mathematical Finance, Imperial College London While the classical theory of arbitrage free pricing has matured, and is now well understood and used by the finance industry, the theory of BSDEs continues to enjoy a rapid growth and remains a domain restricted to academic researchers and a handful of practitioners. Crépey’s book presents this novel approach to a wider community of researchers involved in mathematical modeling in finance. It is clearly an essential reference for anyone interested in the latest developments in financial mathematics. Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance

Martingale Methods in Financial Modelling

Martingale Methods in Financial Modelling
A Book

by Marek Musiela

  • Publisher : Springer Science & Business Media
  • Release : 2013-06-29
  • Pages : 513
  • ISBN : 3662221322
  • Language : En, Es, Fr & De
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A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.

Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes

Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes
A Book

by Cornelis W Oosterlee,Lech A Grzelak

  • Publisher : World Scientific
  • Release : 2019-10-29
  • Pages : 576
  • ISBN : 1786347962
  • Language : En, Es, Fr & De
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This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.

Stochastic Calculus and Financial Applications

Stochastic Calculus and Financial Applications
A Book

by J. Michael Steele

  • Publisher : Springer Science & Business Media
  • Release : 2001
  • Pages : 300
  • ISBN : 9780387950167
  • Language : En, Es, Fr & De
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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

Stochastic Calculus for Finance I

Stochastic Calculus for Finance I
The Binomial Asset Pricing Model

by Steven Shreve

  • Publisher : Springer Science & Business Media
  • Release : 2005-06-28
  • Pages : 187
  • ISBN : 9780387249681
  • Language : En, Es, Fr & De
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Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance

Financial Modelling with Jump Processes

Financial Modelling with Jump Processes
A Book

by Peter Tankov

  • Publisher : CRC Press
  • Release : 2003-12-30
  • Pages : 552
  • ISBN : 1135437947
  • Language : En, Es, Fr & De
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WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Stochastic Modeling

Stochastic Modeling
Analysis and Simulation

by Barry L. Nelson

  • Publisher : Courier Corporation
  • Release : 2012-10-11
  • Pages : 336
  • ISBN : 0486139948
  • Language : En, Es, Fr & De
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Coherent introduction to techniques also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Includes formulation of models, analysis, and interpretation of results. 1995 edition.