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Consistency Problems for Heath-Jarrow-Morton Interest Rate Models

2004-11-02 Mathematics
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Release : 2004-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 48X/5 ( reviews)

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Book Synopsis Consistency Problems for Heath-Jarrow-Morton Interest Rate Models by : Damir Filipovic

Download or read book Consistency Problems for Heath-Jarrow-Morton Interest Rate Models written by Damir Filipovic. This book was released on 2004-11-02. Available in PDF, EPUB and Kindle. Book excerpt: Bond markets differ in one fundamental aspect from standard stock markets. While the latter are built up to a finite number of trade assets, the underlying basis of a bond market is the entire term structure of interest rates: an infinite-dimensional variable which is not directly observable. On the empirical side, this necessitates curve-fitting methods for the daily estimation of the term structure. Pricing models, on the other hand, are usually built upon stochastic factors representing the term structure in a finite-dimensional state space. Written for readers with knowledge in mathematical finance (in particular interest rate theory) and elementary stochastic analysis, this research monograph has threefold aims: to bring together estimation methods and factor models for interest rates, to provide appropriate consistency conditions and to explore some important examples.

Consistency Problems for HJM Interest Rate Models

2000
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Release : 2000
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Consistency Problems for HJM Interest Rate Models by : Damir Filipovic

Download or read book Consistency Problems for HJM Interest Rate Models written by Damir Filipovic. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Cauchy Problems in Infinite Dimensions

2018-09-03 Mathematics
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Release : 2018-09-03
Genre : Mathematics
Kind : eBook
Book Rating : 268/5 ( reviews)

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Book Synopsis Stochastic Cauchy Problems in Infinite Dimensions by : Irina V. Melnikova

Download or read book Stochastic Cauchy Problems in Infinite Dimensions written by Irina V. Melnikova. This book was released on 2018-09-03. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.

Arbitrage Theory in Continuous Time

2004-03 Arbitrage
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Release : 2004-03
Genre : Arbitrage
Kind : eBook
Book Rating : 84X/5 ( reviews)

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Book Synopsis Arbitrage Theory in Continuous Time by : Tomas Björk

Download or read book Arbitrage Theory in Continuous Time written by Tomas Björk. This book was released on 2004-03. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sounds mathematical principles with economic applications. Concentrating on the probabilistics 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 measure theory, probability theory, Girsanov transformations, LIBOR and swap market models, and martingale representations, providing two full treatments of arbitrage pricing: the classical delta-hedging and the modern martingales. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.

Arbitrage Theory in Continuous Time

2020-01-16 Arbitrage
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Release : 2020-01-16
Genre : Arbitrage
Kind : eBook
Book Rating : 618/5 ( reviews)

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Book Synopsis Arbitrage Theory in Continuous Time by : Tomas Bjork

Download or read book Arbitrage Theory in Continuous Time written by Tomas Bjork. This book was released on 2020-01-16. Available in PDF, EPUB and Kindle. Book excerpt: The fourth edition of this widely used textbook on pricing and hedging of financial derivatives now also includes dynamic equilibrium theory and continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, Arbitrage Theory in Continuous Time is designed for graduate students in economics and mathematics, and combines the 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. All concepts and ideas are discussed, not only from a mathematics point of view, but with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Bjork has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. This edition includes an entirely new section presenting dynamic equilibrium theory, covering unit net supply endowments models and the Cox-Ingersoll-Ross equilibrium factor model. Providing two full treatments of arbitrage theory-the classical delta hedging approach and the modern martingale approach-this book is written so that these approaches can be studied independently of each other, thus providing the less mathematically-oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action. This textbook is a natural choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in the market.

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