Search results for: the-foundations-of-continuous-time-finance

A Survey of the Mathematical Foundations of Continuous Time Finance

Author : Peter Umberto Vinella
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The Foundations of Continuous Time Finance

Author : Stephen M. Schaefer
File Size : 87.25 MB
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This volume is an authoritative collection of 25 key papers in the development of continuous time finance. Its five sections cover the continuous time model, dynamic portfolio selection, equilibrium models, derivative pricing and, finally, term structure and other applications. It includes seminal contributions in areas such as: the Martingale approach to no-arbitrage pricing; dynamic models of consumption and portfolio selection; the inter-temporal and consumption based asset pricing models; contingent claims pricing; the term structure of interest rates and the use of changes in numeraire in options pricing. This book will be an essential source of reference for students and researchers in finance and, indeed, anyone needing access to the key papers in this important field.

General Equilibrium Foundations and Continuous time Finance for Heterogeneous and International Economies

Author : Oliver Berndt
File Size : 65.57 MB
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The Economics of Continuous Time Finance

Author : Bernard Dumas
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An introduction to economic applications of the theory of continuous-time finance that strikes a balance between mathematical rigor and economic interpretation of financial market regularities. 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.

Game Theoretic Foundations for Probability and Finance

Author : Glenn Shafer
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Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University

Risk Neutral Valuation

Author : Nicholas H. Bingham
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This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.

Intermediate Financial Theory

Author : Jean-Pierre Danthine (Prof.)
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Targeting readers with backgrounds in economics, Intermediate Financial Theory, Third Edition includes new material on the asset pricing implications of behavioral finance perspectives, recent developments in portfolio choice, derivatives-risk neutral pricing research, and implications of the 2008 financial crisis. Each chapter concludes with questions, and for the first time a freely accessible website presents complementary and supplementary material for every chapter. Known for its rigor and intuition, Intermediate Financial Theory is perfect for those who need basic training in financial theory and those looking for a user-friendly introduction to advanced theory. Completely updated edition of classic textbook that fills a gap between MBA- and PhD-level texts Focuses on clear explanations of key concepts and requires limited mathematical prerequisites Online solutions manual available Updates include new structure emphasizing the distinction between the equilibrium and the arbitrage perspectives on valuation and pricing, and a new chapter on asset management for the long-term investor

Market Risk Analysis Quantitative Methods in Finance

Author : Carol Alexander
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Written by leading market risk academic, Professor Carol Alexander, Quantitative Methods in Finance forms part one of the Market Risk Analysis four volume set. Starting from the basics, this book helps readers to take the first step towards becoming a properly qualified financial risk manager and asset manager, roles that are currently in huge demand. Accessible to intelligent readers with a moderate understanding of mathematics at high school level or to anyone with a university degree in mathematics, physics or engineering, no prior knowledge of finance is necessary. Instead the emphasis is on understanding ideas rather than on mathematical rigour, meaning that this book offers a fast-track introduction to financial analysis for readers with some quantitative background, highlighting those areas of mathematics that are particularly relevant to solving problems in financial risk management and asset management. Unique to this book is a focus on both continuous and discrete time finance so that Quantitative Methods in Finance is not only about the application of mathematics to finance; it also explains, in very pedagogical terms, how the continuous time and discrete time finance disciplines meet, providing a comprehensive, highly accessible guide which will provide readers with the tools to start applying their knowledge immediately. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Principal component analysis of European equity indices; Calibration of Student t distribution by maximum likelihood; Orthogonal regression and estimation of equity factor models; Simulations of geometric Brownian motion, and of correlated Student t variables; Pricing European and American options with binomial trees, and European options with the Black-Scholes-Merton formula; Cubic spline fitting of yields curves and implied volatilities; Solution of Markowitz problem with no short sales and other constraints; Calculation of risk adjusted performance metrics including generalised Sharpe ratio, omega and kappa indices.

Game Theoretic Foundations for Probability and Finance

Author : Glenn Shafer
File Size : 44.74 MB
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Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk's Probability and Finance , published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito's stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers "Ever since Kolmogorov's Grundbegriffe , the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades." - Peter Grünwald, CWI and University of Leiden "Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors." - Ioannis Karatzas, Columbia University.

Applied Economic Forecasting using Time Series Methods

Author : Eric Ghysels
File Size : 52.89 MB
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Economic forecasting is a key ingredient of decision making both in the public and in the private sector. Because economic outcomes are the result of a vast, complex, dynamic and stochastic system, forecasting is very difficult and forecast errors are unavoidable. Because forecast precision and reliability can be enhanced by the use of proper econometric models and methods, this innovative book provides an overview of both theory and applications. Undergraduate and graduate students learning basic and advanced forecasting techniques will be able to build from strong foundations, and researchers in public and private institutions will have access to the most recent tools and insights. Readers will gain from the frequent examples that enhance understanding of how to apply techniques, first by using stylized settings and then by real data applications--focusing on macroeconomic and financial topics. This is first and foremost a book aimed at applying time series methods to solve real-world forecasting problems. Applied Economic Forecasting using Time Series Methods starts with a brief review of basic regression analysis with a focus on specific regression topics relevant for forecasting, such as model specification errors, dynamic models and their predictive properties as well as forecast evaluation and combination. Several chapters cover univariate time series models, vector autoregressive models, cointegration and error correction models, and Bayesian methods for estimating vector autoregressive models. A collection of special topics chapters study Threshold and Smooth Transition Autoregressive (TAR and STAR) models, Markov switching regime models, state space models and the Kalman filter, mixed frequency data models, nowcasting, forecasting using large datasets and, finally, volatility models. There are plenty of practical applications in the book and both EViews and R code are available online at authors' website.

Foundations of Modern Macroeconomics

Author : Ben J. Heijdra
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The study of macroeconomics can seem a daunting project. The field is complex and sometimes poorly defined and there are a variety of competing approaches. It is easy for the senior bachelor and starting master student to get lost in the forest of macroeconomics and the mathematics it uses extensively. Foundations of Modern Macroeconomics is a guide book for the interested and ambitious student. Non-partisan in its approach, it deals with all the major topics, summarising the important approaches and providing the reader with a coherent angle on all aspects of macroeconomic thought. Each chapter deals with a separate area of macroeconomics, and each contains a summary section of key points and a further reading list. Using nothing more than undergraduate mathematical skills, it takes the student from basic IS-LM style macro models to the state of the art literature on Dynamic Stochastic General Equilibrium, explaining the mathematical tricks used where they are first introduced. Fully updated and substantially revised, this third edition of Foundations of Modern Macroeconomics now includes brand new chapters covering highly topical subjects such as dynamic programming, competitive risk sharing equilibria and the New Keynesian DSGE approach.

Financial Markets in Continuous Time

Author : Rose-Anne Dana
File Size : 58.13 MB
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This book explains key financial concepts, mathematical tools and theories of mathematical finance. It is organized in four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of equilibrium theory and applies this in financial markets. The last part tackles market incompleteness and the valuation of exotic options.

Intermediate Financial Theory

Author : Jean-Pierre Danthine
File Size : 23.81 MB
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Targeting readers with backgrounds in economics, Intermediate Financial Theory, Third Edition includes new material on the asset pricing implications of behavioral finance perspectives, recent developments in portfolio choice, derivatives-risk neutral pricing research, and implications of the 2008 financial crisis. Each chapter concludes with questions, and for the first time a freely accessible website presents complementary and supplementary material for every chapter. Known for its rigor and intuition, Intermediate Financial Theory is perfect for those who need basic training in financial theory and those looking for a user-friendly introduction to advanced theory. Completely updated edition of classic textbook that fills a gap between MBA- and PhD-level texts Focuses on clear explanations of key concepts and requires limited mathematical prerequisites Online solutions manual available Updates include new structure emphasizing the distinction between the equilibrium and the arbitrage perspectives on valuation and pricing, and a new chapter on asset management for the long-term investor

Finance in America

Author : Kevin R. Brine
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The history of what we call finance today does not begin in ancient Mesopotamia, or in Imperial China, or in the counting houses of Renaissance Europe. This timely and magisterial book shows that finance as we know it--the combination of institutions, regulations, and models, as well as the infrastructure that manages money, credit, claims, banking, assets, and liabilities--emerged gradually starting in the late nineteenth century and coalesced only after World War II. Kevin Brine, a financial industry veteran, and Mary Poovey, a historian, lay bare the history of finance in the United States over this critical period. They show how modern finance made itself known in episodes such as the 1907 Bankers' Panic on Wall Street, passage of the Federal Reserve Act in 1913, and the marginalist tax policies adopted by the federal government in the 1920s. Over its long history, the distinctive feature of modern economics has been its reliance on mathematical modeling; Brine and Poovey show how this reliance came about, and how economists themselves understand it. "Finance in America: An Unfinished Story" provides the long view that we need to advance our national conversation about the place of finance. The story is unfinished because the 2009 financial crisis opened a perilous new chapter in this history, with reverberations that are still felt throughout the world. How we arrived at this most recent crisis is impossible to understand without the kind of history that Brine and Poovey provide here.

Continuous Time Models in Corporate Finance Banking and Insurance

Author : Santiago Moreno-Bromberg
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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.

Anomalous Transport

Author : Rainer Klages
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This multi-author reference work provides a unique introduction to the currently emerging, highly interdisciplinary field of those transport processes that cannot be described by using standard methods of statistical mechanics. It comprehensively summarizes topics ranging from mathematical foundations of anomalous dynamics to the most recent experiments in this field. In so doing, this monograph extracts and emphasizes common principles and methods from many different disciplines while providing up-to-date coverage of this new field of research, considering such diverse applications as plasma physics, glassy material, cell science, and socio-economic aspects. The book will be of interest to both theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic processes. It also forms an ideal starting point for graduate students moving into this area. 18 chapters written by internationally recognized experts in this field provide in-depth introductions to fundamental aspects of anomalous transport.

Financial Pricing Models in Continuous Time and Kalman Filtering

Author : B.Philipp Kellerhals
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Straight after its invention in the early sixties, the Kalman filter approach became part of the astronautical guidance system of the Apollo project and therefore received immediate acceptance in the field of electrical engineer ing. This sounds similar to the well known success story of the Black-Scholes model in finance, which has been implemented by the Chicago Board of Op tions Exchange (CBOE) within a few month after its publication in 1973. Recently, the Kalman filter approach has been discovered as a comfortable estimation tool in continuous time finance, bringing together seemingly un related methods from different fields. Dr. B. Philipp Kellerhals contributes to this topic in several respects. Specialized versions of the Kalman filter are developed and implemented for three different continuous time pricing models: A pricing model for closed-end funds, taking advantage from the fact, that the net asset value is observable, a term structure model, where the market price of risk itself is a stochastic variable, and a model for electricity forwards, where the volatility of the price process is stochastic. Beside the fact that these three models can be treated independently, the book as a whole gives the interested reader a comprehensive account of the requirements and capabilities of the Kalman filter applied to finance models. While the first model uses a linear version of the filter, the second model using LIBOR and swap market data requires an extended Kalman filter. Finally, the third model leads to a non-linear transition equation of the filter algorithm.

Foundations of Computational Finance with MATLAB

Author : Ed McCarthy
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Graduate from Excel to MATLAB® to keep up with the evolution of finance data Foundations of Computational Finance with MATLAB® is an introductory text for both finance professionals looking to branch out from the spreadsheet, and for programmers who wish to learn more about finance. As financial data grows in volume and complexity, its very nature has changed to the extent that traditional financial calculators and spreadsheet programs are simply no longer enough. Today’s analysts need more powerful data solutions with more customization and visualization capabilities, and MATLAB provides all of this and more in an easy-to-learn skillset. This book walks you through the basics, and then shows you how to stretch your new skills to create customized solutions. Part I demonstrates MATLAB’s capabilities as they apply to traditional finance concepts, and PART II shows you how to create interactive and reusable code, link with external data sources, communicate graphically, and more. Master MATLAB’s basic operations including matrices, arrays, and flexible data structures Learn how to build your own customized solutions when the built-ins just won’t do Learn how to handle financial data and industry-specific variables including risk and uncertainty Adopt more accurate modeling practices for portfolios, options, time series, and more MATLAB is an integrated development environment that includes everything you need in one well-designed user interface. Available Toolboxes provide tested algorithms that save you hours of code, and the skills you learn using MATLAB make it easier to learn additional languages if you choose to do so. Financial firms are catching up to universities in MATLAB usage, so this is skill set that will follow you throughout your career. When you’re ready to step into the new age of finance, Foundations of Computational Finance with MATLAB provides the expert instruction you need to get started quickly.

Continuous Time Asset Pricing Theory

Author : Robert A. Jarrow
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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.

Game Theoretic Foundations for Probability and Finance

Author : Glenn Shafer
File Size : 22.11 MB
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Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk’s Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito’s stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers “Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades.” – Peter Grünwald, CWI and University of Leiden “Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors.” – Ioannis Karatzas, Columbia University