Springer Finance – serie

This work is aimed at an audience with a sound mathematical background wishing to learn about the rapidly expanding ?eld of mathematical ?nance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and probability. The emphasis throughout is on developing the mathematical concepts required for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or ‘exotic’) ?nancial - struments that now appear on the derivatives markets; the focus throu- out remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to ?nancial markets. The ?rst ?ve chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by non-arbitrage) is presented in Chapter 1. The unique price for a European option in a single-period binomial model is given and then extended to multi-period binomial models. Chapter 2 introduces the idea of a martingale measure for price processes. Following a discussion of the use of self-?nancing tr- ing strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price p- cess is a martingale.

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.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.  Chapter summaries and detailed illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance.Advanced undergraduates and Masters level students in mathematical finance and financial engineering will find this book useful.   Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

This book describes the modelling of prices of ?nancial assets in a simple d- crete time, discrete state, binomial framework. By avoiding the mathematical technicalitiesofcontinuoustime?nancewehopewehavemadethematerial accessible to a wide audience. Some of the developments and formulae appear here for the ?rst time in book form. We hope our book will appeal to various audiences. These include MBA s- dents,upperlevelundergraduatestudents,beginningdoctoralstudents,qu- titative analysts at a basic level and senior executives who seek material on new developments in ?nance at an accessible level. The basic building block in our book is the one-step binomial model where a known price today can take one of two possible values at a future time, which might, for example, be tomorrow, or next month, or next year. In this simple situation “risk neutral pricing” can be de?ned and the model can be applied to price forward contracts, exchange rate contracts and interest rate derivatives. In a few places we discuss multinomial models to explain the notions of incomplete markets and how pricing can be viewed in such a context, where unique prices are no longer available. The simple one-period framework can then be extended to multi-period m- els.TheCox-Ross-RubinsteinapproximationtotheBlackScholesoptionpr- ing formula is an immediate consequence. American, barrier and exotic - tions can all be discussed and priced using binomial models. More precise modelling issues such as implied volatility trees and implied binomial trees are treated, as well as interest rate models like those due to Ho and Lee; and Black, Derman and Toy.

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.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.  Chapter summaries and detailed illustrations are included. Classroom tested exercises conclude every chapter. Some of these extend the theory and others are drawn from practical problems in quantitative finance.Advanced undergraduates and Masters level students in mathematical finance and financial engineering will find this book useful.   Steven E. Shreve is Co-Founder of the Carnegie Mellon MS Program in Computational Finance and winner of the Carnegie Mellon Doherty Prize for sustained contributions to education.

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time.Master's level studentsand researchers in mathematical finance and financial engineering will find this book useful.

In the past three decades, great progress has been made in the theory and prac­ tice of financial derivative securities. Now huge volumes of financial derivative securities are traded on the market every day. This causes a big demand for experts who know how to price financial derivative securities. This book is designed as a textbook for graduate students in a mathematical finance pro­ gram and as a reference book for the people who already work in this field. We hope that a person who has studied this book and who knows how to write codes for engineering computation can handle the business of providing efficient derivative-pricing codes. In order for this book to be used by various people, the prerequisites to study the majority of this book are multivariable calculus, linear algebra, and basic probability and statistics. In this book, the determination of the prices of financial derivative secu­ rities is reduced to solving partial differential equation problems, i. e. , a PDE approach is adopted in order to find the price of a derivative security. This book is divided into two parts. In the first part, we discuss how to establish the corresponding partial differential equations and find the final and nec­ essary boundary conditions for a specific derivative product. If possible, we derive its explicit solution and describe some properties of the solution. In many cases, no explicit solution has been found so far.

This work is aimed at an audience with a sound mathematical background wishing to learn about the rapidly expanding ?eld of mathematical ?nance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and probability. The emphasis throughout is on developing the mathematical concepts required for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or ‘exotic’) ?nancial - struments that now appear on the derivatives markets; the focus throu- out remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to ?nancial markets. The ?rst ?ve chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by non-arbitrage) is presented in Chapter 1. The unique price for a European option in a single-period binomial model is given and then extended to multi-period binomial models. Chapter 2 introduces the idea of a martingale measure for price processes. Following a discussion of the use of self-?nancing tr- ing strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price p- cess is a martingale.

This book describes the modelling of prices of ?nancial assets in a simple d- crete time, discrete state, binomial framework. By avoiding the mathematical technicalitiesofcontinuoustime?nancewehopewehavemadethematerial accessible to a wide audience. Some of the developments and formulae appear here for the ?rst time in book form. We hope our book will appeal to various audiences. These include MBA s- dents,upperlevelundergraduatestudents,beginningdoctoralstudents,qu- titative analysts at a basic level and senior executives who seek material on new developments in ?nance at an accessible level. The basic building block in our book is the one-step binomial model where a known price today can take one of two possible values at a future time, which might, for example, be tomorrow, or next month, or next year. In this simple situation “risk neutral pricing” can be de?ned and the model can be applied to price forward contracts, exchange rate contracts and interest rate derivatives. In a few places we discuss multinomial models to explain the notions of incomplete markets and how pricing can be viewed in such a context, where unique prices are no longer available. The simple one-period framework can then be extended to multi-period m- els.TheCox-Ross-RubinsteinapproximationtotheBlackScholesoptionpr- ing formula is an immediate consequence. American, barrier and exotic - tions can all be discussed and priced using binomial models. More precise modelling issues such as implied volatility trees and implied binomial trees are treated, as well as interest rate models like those due to Ho and Lee; and Black, Derman and Toy.

Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes.This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time.Master's level studentsand researchers in mathematical finance and financial engineering will find this book useful.

Financial Markets Theory presents classical asset pricing theory, a theory composed of milestones such as portfolio selection, risk aversion, fundamental asset pricing theorem, portfolio frontier, CAPM, CCAPM, APT, the Modigliani-Miller Theorem, no arbitrage/risk neutral evaluation and information in financial markets. Starting from an analysis of the empirical tests of the above theories, the author provides a discussion of the most recent literature, pointing out the main advancements within classical asset pricing theory and the new approaches designed to address open problems (e.g. behavioural finance). It is the only textbook to address the economic foundations of financial markets theory from a mathematically rigorous standpoint, and to offer a self-contained critical discussion, based on empirical results. Financial Markets Theory is an advanced book, well-suited for a first graduate course in financial markets, economics or financial mathematics. It is self-contained and introduces topics in a setting accessible to economists and practitioners equipped with a basic mathematical background. For those not acquainted with standard microeconomic theory, the tools needed to follow the analysis are presented early in the book. The approach makes this a vital handbook for practitioners in insurance, banking, investment funds and financial consultancy, as well as an excellent graduate-reference textbook.

Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.

Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo.Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution.

This work, now in a thoroughly revised second edition, presents the economic foundations of financial markets theory from a mathematically rigorous standpoint and offers a self-contained critical discussion based on empirical results. It is the only textbook on the subject to include more than two hundred exercises, with detailed solutions to selected exercises.Financial Markets Theory covers classical asset pricing theory in great detail, including utility theory, equilibrium theory, portfolio selection, mean-variance portfolio theory, CAPM, CCAPM, APT, and the Modigliani-Miller theorem. Starting from an analysis of the empirical evidence on the theory, the authors provide a discussion of the relevant literature, pointing out the main advances in classical asset pricing theory and the new approaches designed to address asset pricing puzzles and open problems (e.g., behavioral finance). Later chapters in the book contain more advanced material, including on the role of information in financial markets, non-classical preferences, noise traders and market microstructure.This textbook is aimed at graduate students in mathematical finance and financial economics, but also serves as a useful reference for practitioners working in insurance, banking, investment funds and financial consultancy. Introducing necessary tools from microeconomic theory, this book is highly accessible and completely self-contained.Advance praise for the second edition:"Financial Markets Theory is comprehensive, rigorous, and yet highly accessible. With their second edition, Barucci and Fontana have set an even higher standard!"Darrell Duffie, Dean Witter Distinguished Professor of Finance, Graduate School of Business, Stanford University"This comprehensive book is a great self-contained source for studying most major theoretical aspects of financial economics. What makes the book particularly useful is that it provides a lot of intuition, detailed discussions of empirical implications, a very thorough survey of the related literature, and many completely solved exercises. The second edition covers more ground and provides many more proofs, and it will be a handy addition to the library of every student or researcher in the field."Jaksa Cvitanic, Richard N. Merkin Professor of Mathematical Finance, Caltech"The second edition of Financial Markets Theory by Barucci and Fontana is a superb achievement that knits together all aspects of modern finance theory, including financial markets microstructure, in a consistent and self-contained framework. Many exercises, together with their detailed solutions, make this book indispensable for serious students in finance."Michel Crouhy, Head of Research and Development, NATIXIS

This work, now in a thoroughly revised second edition, presents the economic foundations of financial markets theory from a mathematically rigorous standpoint and offers a self-contained critical discussion based on empirical results. It is the only textbook on the subject to include more than two hundred exercises, with detailed solutions to selected exercises.Financial Markets Theory covers classical asset pricing theory in great detail, including utility theory, equilibrium theory, portfolio selection, mean-variance portfolio theory, CAPM, CCAPM, APT, and the Modigliani-Miller theorem. Starting from an analysis of the empirical evidence on the theory, the authors provide a discussion of the relevant literature, pointing out the main advances in classical asset pricing theory and the new approaches designed to address asset pricing puzzles and open problems (e.g., behavioral finance). Later chapters in the book contain more advanced material, including on the role of information in financial markets, non-classical preferences, noise traders and market microstructure.This textbook is aimed at graduate students in mathematical finance and financial economics, but also serves as a useful reference for practitioners working in insurance, banking, investment funds and financial consultancy. Introducing necessary tools from microeconomic theory, this book is highly accessible and completely self-contained.Advance praise for the second edition:"Financial Markets Theory is comprehensive, rigorous, and yet highly accessible. With their second edition, Barucci and Fontana have set an even higher standard!"Darrell Duffie, Dean Witter Distinguished Professor of Finance, Graduate School of Business, Stanford University"This comprehensive book is a great self-contained source for studying most major theoretical aspects of financial economics. What makes the book particularly useful is that it provides a lot of intuition, detailed discussions of empirical implications, a very thorough survey of the related literature, and many completely solved exercises. The second edition covers more ground and provides many more proofs, and it will be a handy addition to the library of every student or researcher in the field."Jaksa Cvitanic, Richard N. Merkin Professor of Mathematical Finance, Caltech"The second edition of Financial Markets Theory by Barucci and Fontana is a superb achievement that knits together all aspects of modern finance theory, including financial markets microstructure, in a consistent and self-contained framework. Many exercises, together with their detailed solutions, make this book indispensable for serious students in finance."Michel Crouhy, Head of Research and Development, NATIXIS

This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems.In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods in financial derivatives. For this new edition, the book has been updated throughout with many new problems added. More details about numerical methods for some options, for example, Asian options with discrete sampling, are provided and the proof of solution-uniqueness of derivative security problems and the complete stability analysis of numerical methods for two-dimensional problems are added.  Review of first edition:“…the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS

This book is mainly devoted to finite difference numerical methods for solving partial differential equations (PDEs) models of pricing a wide variety of financial derivative securities. With this objective, the book is divided into two main parts.In the first part, after an introduction concerning the basics on derivative securities, the authors explain how to establish the adequate PDE boundary value problems for different sets of derivative products (vanilla and exotic options, and interest rate derivatives). For many option problems, the analytic solutions are also derived with details. The second part is devoted to explaining and analyzing the application of finite differences techniques to the financial models stated in the first part of the book. For this, the authors recall some basics on finite difference methods, initial boundary value problems, and (having in view financial products with early exercise feature) linear complementarity and free boundary problems.In each chapter, the techniques related to these mathematical and numerical subjects are applied to a wide variety of financial products. This is a textbook for graduate students following a mathematical finance program as well as a valuable reference for those researchers working in numerical methods in financial derivatives. For this new edition, the book has been updated throughout with many new problems added. More details about numerical methods for some options, for example, Asian options with discrete sampling, are provided and the proof of solution-uniqueness of derivative security problems and the complete stability analysis of numerical methods for two-dimensional problems are added.  Review of first edition:“…the book is highly well designed and structured as a textbook for graduate students following a mathematical finance program, which includes Black-Scholes dynamic hedging methodology to price financial derivatives. Also, it is a very valuable reference for those researchers working in numerical methods in financial derivatives, either with a more financial or mathematical background." -- MATHEMATICAL REVIEWS

Non-Gaussian distributions are the key theme of this book which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The aim is to bridge the gap between theoretical developments and the practical implementations of what many users and researchers perceive as "sophisticated" models. The emphasis throughout is on practice: there are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series, such as exchange and interest rates. This book will be an essential reference for practitioners in the finance industry, especially those responsible for managing portfolios and monitoring financial risk, but it will also be useful for mathematicians who want to know more about how their mathematical tools are applied in finance, and as a text for advanced courses in empirical finance; financial econometrics and financial derivatives.

Non-Gaussian distributions are the key theme of this book which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The aim is to bridge the gap between theoretical developments and the practical implementations of what many users and researchers perceive as "sophisticated" models. The emphasis throughout is on practice: there are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series, such as exchange and interest rates. This book will be an essential reference for practitioners in the finance industry, especially those responsible for managing portfolios and monitoring financial risk, but it will also be useful for mathematicians who want to know more about how their mathematical tools are applied in finance, and as a text for advanced courses in empirical finance; financial econometrics and financial derivatives.

Efficient Methods for Valuing Interest Rate Derivatives provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore the practical issues, such as the implementation of models, and model selection.Aimed at people with a solid quantitative background, this book will be of particular interest to risk managers, interest rate derivative traders, quantitative researchers, portfolio and fund managers, and students of mathematics and economics, but it will also prove invaluable to anyone looking for a good overview of interest rate derivative modelling.

Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be an important tool in the pricing and hedging of financial derivatives. Following the success of the first edition of ‘Risk-Neutral Valuation’, the authors have thoroughly revised the entire book, taking into account recent developments in the field, and changes in their own thinking and teaching. In particular, the chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on: ·Infinite divisibility and Lévy processes ·Lévy-based models in incomplete markets Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.

Self-organizing maps (SOM) have proven to be of significant economic value in the areas of finance, economic and marketing applications. As a result, this area is rapidly becoming a non-academic technology. This book looks at near state-of-the-art SOM applications in the above areas, and is a multi-authored volume, edited by Guido Deboeck, a leading exponent in the use of computational methods in financial and economic forecasting, and by the originator of SOM, Teuvo Kohonen. The book contains chapters on applications of unsupervised neural networks using Kohonen's self-organizing map approach.

Efficient Methods for Valuing Interest Rate Derivatives provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore the practical issues, such as the implementation of models, and model selection.Aimed at people with a solid quantitative background, this book will be of particular interest to risk managers, interest rate derivative traders, quantitative researchers, portfolio and fund managers, and students of mathematics and economics, but it will also prove invaluable to anyone looking for a good overview of interest rate derivative modelling.

Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.

Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be an important tool in the pricing and hedging of financial derivatives. Following the success of the first edition of ‘Risk-Neutral Valuation’, the authors have thoroughly revised the entire book, taking into account recent developments in the field, and changes in their own thinking and teaching. In particular, the chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on: ·Infinite divisibility and Lévy processes ·Lévy-based models in incomplete markets Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.

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.

Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field.Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.

Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field.Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.

Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features ​new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.

This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications.In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s currentand future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences.Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.