The Economics of Continuous Time Finance

The Economics of Continuous Time Finance

This book introduces the economic applications of the theory of continuous-time finance, with the goal of enabling the construction of realistic models, particularly those involving incomplete markets.

Author: Bernard Dumas

Publisher: MIT Press

ISBN: 9780262036542

Category: Business & Economics

Page: 640

View: 221

This book introduces the economic applications of the theory of continuous-time finance, with the goal of enabling the construction of realistic models, particularly those involving incomplete markets. Indeed, most recent applications of continuous-time finance aim to capture the imperfections and dysfunctions of financial markets -- characteristics that became especially apparent during the market turmoil that started in 2008. The book begins by using discrete time to illustrate the basic mechanisms and introduce such notions as completeness, redundant pricing, and no arbitrage. It develops the continuous-time analog of those mechanisms and introduces the powerful tools of stochastic calculus. Going beyond other textbooks, the book then focuses on the study of markets in which some form of incompleteness, volatility, heterogeneity, friction, or behavioral subtlety arises. After presenting solutions methods for control problems and related partial differential equations, the text examines portfolio optimization and equilibrium in incomplete markets, interest rate and fixed-income modeling, and stochastic volatility. Finally, it presents models where investors form different beliefs or suffer frictions, form habits, or have recursive utilities, studying the effects not only on optimal portfolio choices but also on equilibrium, or the price of primitive securities. The book strikes a balance between mathematical rigor and the need for economic interpretation of financial market regularities, although with an emphasis on the latter.
Categories: Business & Economics

Continuous Time Finance

Continuous Time Finance

For this revised edition a new section on managing university endowments has been added. The book begins with a foreword by Paul Samuelson.

Author: Robert C. Merton

Publisher: Wiley-Blackwell

ISBN: 0631185089

Category: Business & Economics

Page: 754

View: 992

Robert C. Merton's widely-used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual finance choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance.
Categories: Business & Economics

Continuous Time Asset Pricing Theory

Continuous Time Asset Pricing Theory

Yielding new insights into important market phenomena like asset price bubbles and trading constraints, this is the first textbook to present asset pricing theory using the martingale approach (and all of its extensions).

Author: Robert A. Jarrow

Publisher: Springer

ISBN: 9783319778211

Category: Mathematics

Page: 448

View: 812

Yielding new insights into important market phenomena like asset price bubbles and trading constraints, this is the first textbook to present asset pricing theory using the martingale approach (and all of its extensions). Since the 1970s asset pricing theory has been studied, refined, and extended, and many different approaches can be used to present this material. Existing PhD–level books on this topic are aimed at either economics and business school students or mathematics students. While the first mostly ignore much of the research done in mathematical finance, the second emphasizes mathematical finance but does not focus on the topics of most relevance to economics and business school students. These topics are derivatives pricing and hedging (the Black–Scholes–Merton, the Heath–Jarrow–Morton, and the reduced-form credit risk models), multiple-factor models, characterizing systematic risk, portfolio optimization, market efficiency, and equilibrium (capital asset and consumption) pricing models. This book fills this gap, presenting the relevant topics from mathematical finance, but aimed at Economics and Business School students with strong mathematical backgrounds.
Categories: Mathematics

Financial Markets in Continuous Time

Financial Markets in Continuous Time

Econometrica, 54, 1161–1183 Duffie, D. (1987): Stochastic equilibria with
incomplete financial markets. Journal of Economic Theory, 41, 405–416 Duffie, D
. (1988): An extension of the Black–Scholes model of security valuation. Journal
of ...

Author: Rose-Anne Dana

Publisher: Springer Science & Business Media

ISBN: 9783540711490

Category: Business & Economics

Page: 324

View: 174

This book explains key financial concepts, mathematical tools and theories of mathematical finance. The range of topics covered is very broad for an introductory text. The book contains two separate appendices on Brownian motion and on numerical methods.
Categories: Business & Economics

Arbitrage Theory in Continuous Time

Arbitrage Theory in Continuous Time

The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications.

Author: Tomas Björk

Publisher: OUP Oxford

ISBN: 9780191610295

Category: Business & Economics

Page: 560

View: 677

The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
Categories: Business & Economics

Stochastic Calculus for Finance I

Stochastic Calculus for Finance I

This book is being published in two volumes. The first volume presents the binomial asset-pricing model primarily as a vehicle for introducing in the simple setting the concepts needed for the continuous-time theory in the second volume.

Author: Steven Shreve

Publisher: Springer Science & Business Media

ISBN: 0387249680

Category: Mathematics

Page: 187

View: 108

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
Categories: Mathematics

Continuous Time Models in Corporate Finance Banking and Insurance

Continuous Time Models in Corporate Finance  Banking  and Insurance

The book concludes by presenting the dynamic agency model, where financial frictions stem from the lack of interest alignment between a firm's manager and its financiers.

Author: Santiago Moreno-Bromberg

Publisher: Princeton University Press

ISBN: 9781400889204

Category: Business & Economics

Page: 176

View: 289

Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition, Santiago Moreno-Bromberg and Jean-Charles Rochet analyze corporate decisions such as dividend distribution, the issuance of securities, and capital structure and default. They pay particular attention to financial intermediaries, including banks and insurance companies. The authors begin by recalling the ways that option-pricing techniques can be employed for the pricing of corporate debt and equity. They then present the dynamic model of the trade-off between taxes and bankruptcy costs and derive implications for optimal capital structure. The core chapter introduces the workhorse liquidity-management model—where liquidity and risk management decisions are made in order to minimize the costs of external finance. This model is used to study corporate finance decisions and specific features of banks and insurance companies. The book concludes by presenting the dynamic agency model, where financial frictions stem from the lack of interest alignment between a firm's manager and its financiers. The appendix contains an overview of the main mathematical tools used throughout the book. Requiring some familiarity with stochastic calculus methods, Continuous-Time Models in Corporate Finance will be useful for students, researchers, and professionals who want to develop dynamic models of firms' financial decisions.
Categories: Business & Economics

Continuous Time Approach to Financial Volatility

Continuous Time Approach to Financial Volatility

The idea of this book is to explain how Levy processes can be used to study some problems in finance.

Author: Ole E. Barndorff-Nielsen

Publisher:

ISBN: 0521834406

Category: Business & Economics

Page: 400

View: 616

The idea of this book is to explain how Levy processes can be used to study some problems in finance. The necessary technology is motivated and justified in an opening chapter, and is then followed by chapters explaining the mathematics and computational aspects of the subject. The heart of the book describes applications, with further mathematical ideas introduced as and when needed. The authors cover new ideas not presented in book form before, blending theory and practice, and this account will be of value to all those working in mathematical finance, financial econometrics, probability and statistics."
Categories: Business & Economics

Financial Pricing Models in Continuous Time and Kalman Filtering

Financial Pricing Models in Continuous Time and Kalman Filtering

The volume Financial Pricing Models in Continuous Time and Kalman Filtering provides a framework that shows how to bridge the gap between the time-continuous pricing practice in financial engineering and the capital market data inevitably ...

Author: B. Philipp Kellerhals

Publisher: Springer Science & Business Media

ISBN: UCSC:32106018575446

Category: Business & Economics

Page: 247

View: 728

The modern field of financial economics asks for sound pricing models grounded on the theory of financial decision making as well as for accurate estimation techniques when it comes to empirical inferences of the specified model. The volume Financial Pricing Models in Continuous Time and Kalman Filtering provides a framework that shows how to bridge the gap between the time-continuous pricing practice in financial engineering and the capital market data inevitably only available at discrete time intervals. Starting with the general framework we consider applications to financial instruments traded on the markets for funds, fixed income products, and electricity derivatives.
Categories: Business & Economics

Incomplete Information and Heterogeneous Beliefs in Continuous time Finance

Incomplete Information and Heterogeneous Beliefs in Continuous time Finance

Federal Reserve Finance and Economics Discussion Series No. 1999-47 ...
Princeton University Press, Princeton NJ Duffie, D., Sun, T.-S. (1990): Transaction
Costs and Portfolio Choice in a Discrete-Continuous Time Setting. Journal of ...

Author: Alexandre C. Ziegler

Publisher: Springer Science & Business Media

ISBN: 9783540247555

Category: Business & Economics

Page: 198

View: 966

After a brief review of the existing incomplete information literature, the effect of incomplete information on investors' exptected utility, risky asset prices, and interest rates is described. It is demonstrated that increasing the quality of investors' information need not increase their expected utility and the prices of risky assets. The impact of other factors is discussed in detail. It is also demonstrated that financial markets in general do not aggregate information efficiently, a fact that can explain the equity premium puzzle.
Categories: Business & Economics

Contract Theory in Continuous Time Models

Contract Theory in Continuous Time Models

In recent years there has been a significant increase of interest in continuous-time Principal-Agent models, or contract theory, and their applications.

Author: Jakša Cvitanic

Publisher: Springer Science & Business Media

ISBN: 9783642142000

Category: Mathematics

Page: 256

View: 341

In recent years there has been a significant increase of interest in continuous-time Principal-Agent models, or contract theory, and their applications. Continuous-time models provide a powerful and elegant framework for solving stochastic optimization problems of finding the optimal contracts between two parties, under various assumptions on the information they have access to, and the effect they have on the underlying "profit/loss" values. This monograph surveys recent results of the theory in a systematic way, using the approach of the so-called Stochastic Maximum Principle, in models driven by Brownian Motion. Optimal contracts are characterized via a system of Forward-Backward Stochastic Differential Equations. In a number of interesting special cases these can be solved explicitly, enabling derivation of many qualitative economic conclusions.
Categories: Mathematics

Finance in Continuous Time

Finance in Continuous Time

Finance in Continuous Time provides a brief introduction to the subject for finance faculty, students in finance, and finance professionals who do not specialize in continous time methods.

Author: David Shimko

Publisher: Wiley-Blackwell

ISBN: 1878975072

Category: Business & Economics

Page: 110

View: 669

Finance in Continuous Time provides a brief introduction to the subject for finance faculty, students in finance, and finance professionals who do not specialize in continous time methods.
Categories: Business & Economics

Financial Asset Pricing Theory

Financial Asset Pricing Theory

The book presents models for the pricing of financial assets such as stocks, bonds, and options.

Author: Claus Munk

Publisher: Oxford University Press

ISBN: 9780199585496

Category: Business & Economics

Page: 585

View: 552

The book presents models for the pricing of financial assets such as stocks, bonds, and options. The models are formulated and analyzed using concepts and techniques from mathematics and probability theory. It presents important classic models and some recent 'state-of-the-art' models that outperform the classics.
Categories: Business & Economics

Introduction to the Economics and Mathematics of Financial Markets

Introduction to the Economics and Mathematics of Financial Markets

The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students.

Author: Jakša Cvitanić

Publisher: MIT Press

ISBN: 0262033208

Category: Business & Economics

Page: 494

View: 573

An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models--a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.
Categories: Business & Economics

Financial Economics Risk And Information 2nd Edition

Financial Economics  Risk And Information  2nd Edition

The objective of this book is to introduce undergraduate and first-year graduate students to the methods and solutions of the main problems in finance theory relating to the economics of uncertainty and information.

Author: Bianconi Marcelo

Publisher: World Scientific Publishing Company

ISBN: 9789814405126

Category: Business & Economics

Page: 496

View: 210

Financial Economics, Risk and Information presents the fundamentals of finance in static and dynamic frameworks with focus on risk and information. The objective of this book is to introduce undergraduate and first-year graduate students to the methods and solutions of the main problems in finance theory relating to the economics of uncertainty and information. The main goal of the second edition is to make the materials more accessible to a wider audience of students and finance professionals. The focus is on developing a core body of theory that will provide the student with a solid intellectual foundation for more advanced topics and methods. The new edition has streamlined chapters and topics, with new sections on portfolio choice under alternative information structures. The starting point is the traditional mean-variance approach, followed by portfolio choice from first principles. The topics are extended to alternative market structures, alternative contractual arrangements and agency, dynamic stochastic general equilibrium in discrete and continuous time, attitudes towards risk and towards inter-temporal substitution in discrete and continuous time; and option pricing. In general, the book presents a balanced introduction to the use of stochastic methods in discrete and continuous time in the field of financial economics.
Categories: Business & Economics

Continuous time Stochastic Control and Optimization with Financial Applications

Continuous time Stochastic Control and Optimization with Financial Applications

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 ...

Author: Huyên Pham

Publisher: Springer Science & Business Media

ISBN: 9783540895008

Category: Mathematics

Page: 232

View: 601

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.
Categories: Mathematics

Stochastic Finance

Stochastic Finance

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.

Author: Nicolas Privault

Publisher: CRC Press

ISBN: 9781466594029

Category: Business & Economics

Page: 441

View: 950

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.
Categories: Business & Economics

An Introduction to Continuous Time Stochastic Processes

An Introduction to Continuous Time Stochastic Processes

Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes.

Author: Vincenzo Capasso

Publisher: Springer Science & Business Media

ISBN: 9780817683467

Category: Mathematics

Page: 434

View: 803

Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.
Categories: Mathematics

Optimization in Economics and Finance

Optimization in Economics and Finance

... the other models in this book, assume new3 economics, and may be applied to
social choice for an optimal intertemporal allocation of financial and physical
resources in the economy. Should such a model be in discrete or continuous time
?

Author: Bruce D. Craven

Publisher: Springer Science & Business Media

ISBN: 9780387242804

Category: Business & Economics

Page: 161

View: 861

Some recent developments in the mathematics of optimization, including the concepts of invexity and quasimax, have not yet been applied to models of economic growth, and to finance and investment. Their applications to these areas are shown in this book.
Categories: Business & Economics

Financial Pricing Models in Continuous Time and Kalman Filtering

Financial Pricing Models in Continuous Time and Kalman Filtering

Author: B. Philipp Kellerhals

Publisher: Springer Science & Business Media

ISBN: STANFORD:36105029816746

Category: Business & Economics

Page: 247

View: 522

The modern field of financial economics asks for sound pricing models grounded on the theory of financial decision making as well as for accurate estimation techniques when it comes to empirical inferences of the specified model. The volume Financial Pricing Models in Continuous Time and Kalman Filtering provides a framework that shows how to bridge the gap between the time-continuous pricing practice in financial engineering and the capital market data inevitably only available at discrete time intervals. Starting with the general framework we consider applications to financial instruments traded on the markets for funds, fixed income products, and electricity derivatives.
Categories: Business & Economics