The Foundations Of Continuous Time Finance

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The Foundations of Continuous Time Finance

Stephen M. Schaefer
The Foundations of Continuous Time Finance Book PDF

Author : Stephen M. Schaefer
Publisher : Edward Elgar Publishing
Page : 0 pages
File Size : 47,8 Mb
Release : 2001
Category : Finance
ISBN : 1858987504

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The Foundations of Continuous Time Finance by Stephen M. Schaefer Pdf

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.

Arbitrage Theory in Continuous Time

Tomas Björk
Arbitrage Theory in Continuous Time Book PDF

Author : Tomas Björk
Publisher : OUP Oxford
Page : 600 pages
File Size : 55,8 Mb
Release : 2009-08-06
Category : Business & Economics
ISBN : 9780191610295

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Arbitrage Theory in Continuous Time by Tomas Björk Pdf

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.

Continuous-Time Finance

Robert C. Merton
Continuous Time Finance Book PDF

Author : Robert C. Merton
Publisher : Wiley-Blackwell
Page : 754 pages
File Size : 41,8 Mb
Release : 1992-11-03
Category : Business & Economics
ISBN : 0631185089

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Continuous-Time Finance by Robert C. Merton Pdf

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.

Financial Markets in Continuous Time

Rose-Anne Dana,Monique Jeanblanc-Picqué,Monique Jeanblanc
Financial Markets in Continuous Time Book PDF

Author : Rose-Anne Dana,Monique Jeanblanc-Picqué,Monique Jeanblanc
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 47,9 Mb
Release : 2007-07-12
Category : Business & Economics
ISBN : 9783540711490

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Financial Markets in Continuous Time by Rose-Anne Dana,Monique Jeanblanc-Picqué,Monique Jeanblanc Pdf

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.

Stochastic Calculus for Finance I

Steven Shreve
Stochastic Calculus for Finance I Book PDF

Author : Steven Shreve
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 49,6 Mb
Release : 2005-06-28
Category : Mathematics
ISBN : 0387249680

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Stochastic Calculus for Finance I by Steven Shreve Pdf

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

The Economics of Continuous-Time Finance

Bernard Dumas,Elisa Luciano
The Economics of Continuous Time Finance Book PDF

Author : Bernard Dumas,Elisa Luciano
Publisher : MIT Press
Page : 641 pages
File Size : 45,7 Mb
Release : 2017-10-27
Category : Business & Economics
ISBN : 9780262036542

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The Economics of Continuous-Time Finance by Bernard Dumas,Elisa Luciano Pdf

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.

Continuous-Time Asset Pricing Theory

Robert A. Jarrow
Continuous Time Asset Pricing Theory Book PDF

Author : Robert A. Jarrow
Publisher : Springer Nature
Page : 470 pages
File Size : 47,8 Mb
Release : 2021-07-30
Category : Business & Economics
ISBN : 9783030744106

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Continuous-Time Asset Pricing Theory by Robert A. Jarrow Pdf

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.

Game-Theoretic Foundations for Probability and Finance

Glenn Shafer,Vladimir Vovk
Game Theoretic Foundations for Probability and Finance Book PDF

Author : Glenn Shafer,Vladimir Vovk
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 54,5 Mb
Release : 2019-03-21
Category : Business & Economics
ISBN : 9781118547939

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Game-Theoretic Foundations for Probability and Finance by Glenn Shafer,Vladimir Vovk Pdf

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

Game-Theoretic Foundations for Probability and Finance

Glenn Shafer,Vladimir Vovk
Game Theoretic Foundations for Probability and Finance Book PDF

Author : Glenn Shafer,Vladimir Vovk
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 49,5 Mb
Release : 2019-05-29
Category : Business & Economics
ISBN : 9780470903056

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Game-Theoretic Foundations for Probability and Finance by Glenn Shafer,Vladimir Vovk Pdf

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

Foundations of Reinforcement Learning with Applications in Finance

Ashwin Rao,Tikhon Jelvis
Foundations of Reinforcement Learning with Applications in Finance Book PDF

Author : Ashwin Rao,Tikhon Jelvis
Publisher : CRC Press
Page : 658 pages
File Size : 51,7 Mb
Release : 2022-12-16
Category : Mathematics
ISBN : 9781000801101

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Foundations of Reinforcement Learning with Applications in Finance by Ashwin Rao,Tikhon Jelvis Pdf

Foundations of Reinforcement Learning with Applications in Finance aims to demystify Reinforcement Learning, and to make it a practically useful tool for those studying and working in applied areas — especially finance. Reinforcement Learning is emerging as a powerful technique for solving a variety of complex problems across industries that involve Sequential Optimal Decisioning under Uncertainty. Its penetration in high-profile problems like self-driving cars, robotics, and strategy games points to a future where Reinforcement Learning algorithms will have decisioning abilities far superior to humans. But when it comes getting educated in this area, there seems to be a reluctance to jump right in, because Reinforcement Learning appears to have acquired a reputation for being mysterious and technically challenging. This book strives to impart a lucid and insightful understanding of the topic by emphasizing the foundational mathematics and implementing models and algorithms in well-designed Python code, along with robust coverage of several financial trading problems that can be solved with Reinforcement Learning. This book has been created after years of iterative experimentation on the pedagogy of these topics while being taught to university students as well as industry practitioners. Features Focus on the foundational theory underpinning Reinforcement Learning and software design of the corresponding models and algorithms Suitable as a primary text for courses in Reinforcement Learning, but also as supplementary reading for applied/financial mathematics, programming, and other related courses Suitable for a professional audience of quantitative analysts or data scientists Blends theory/mathematics, programming/algorithms and real-world financial nuances while always striving to maintain simplicity and to build intuitive understanding To access the code base for this book, please go to: https://github.com/TikhonJelvis/RL-book

Continuous-time Linear Models

John H. Cochrane
Continuous time Linear Models Book PDF

Author : John H. Cochrane
Publisher : Unknown
Page : 76 pages
File Size : 46,6 Mb
Release : 2012
Category : Business & Economics
ISBN : UCSD:31822038808705

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Continuous-time Linear Models by John H. Cochrane Pdf

I translate familiar concepts of discrete-time time-series to contnuous-time equivalent. I cover lag operators, ARMA models, the relation between levels and differences, integration and cointegration, and the Hansen-Sargent prediction formulas.

Financial Mathematics

Giuseppe Campolieti,Roman N. Makarov
Financial Mathematics Book PDF

Author : Giuseppe Campolieti,Roman N. Makarov
Publisher : CRC Press
Page : 662 pages
File Size : 44,9 Mb
Release : 2022-12-21
Category : Business & Economics
ISBN : 9780429889097

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Financial Mathematics by Giuseppe Campolieti,Roman N. Makarov Pdf

The book has been tested and refined through years of classroom teaching experience. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. This textbook provides complete coverage of continuous-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. Key features: In-depth coverage of continuous-time theory and methodology Numerous, fully worked out examples and exercises in every chapter Mathematically rigorous and consistent, yet bridging various basic and more advanced concepts Judicious balance of financial theory and mathematical methods Guide to Material This revision contains: Almost 150 pages worth of new material in all chapters A appendix on probability theory An expanded set of solved problems and additional exercises Answers to all exercises This book is a comprehensive, self-contained, and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics. The text complements Financial Mathematics: A Comprehensive Treatment in Discrete Time, by the same authors, also published by CRC Press.

Stochastic Calculus for Finance II

Steven Shreve
Stochastic Calculus for Finance II Book PDF

Author : Steven Shreve
Publisher : Springer
Page : 0 pages
File Size : 50,5 Mb
Release : 2010-12-01
Category : Mathematics
ISBN : 144192311X

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Stochastic Calculus for Finance II by Steven Shreve Pdf

"A wonderful display of the use of mathematical probability to derive a large set of results from a small set of assumptions. In summary, this is a well-written text that treats the key classical models of finance through an applied probability approach....It should serve as an excellent introduction for anyone studying the mathematics of the classical theory of finance." --SIAM

An Introduction to Continuous-Time Stochastic Processes

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

Author : Vincenzo Capasso,David Bakstein
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 55,5 Mb
Release : 2008-01-03
Category : Mathematics
ISBN : 9780817644284

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

This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. Balancing theory and applications, the authors use stochastic methods and concrete examples to model real-world problems from engineering, biomathematics, biotechnology, and finance. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. The book will be of interest to students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, physics, and engineering.

Risk-Neutral Valuation

Nicholas H. Bingham,Rüdiger Kiesel
Risk Neutral Valuation Book PDF

Author : Nicholas H. Bingham,Rüdiger Kiesel
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 49,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781447138563

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Risk-Neutral Valuation by Nicholas H. Bingham,Rüdiger Kiesel Pdf

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.