Search results for ""Author Ekkehard Kopp""

Book SynopsisFrom Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus.Table of ContentsPreface; 1. Probability and measure; 2. Measures and distribution functions; 3. Measurable functions/random variables; 4. Integration and expectation; 5. Lp-spaces and conditional expectation; 6. Discrete-time martingales; 7. Brownian motion; 8. Stochastic integrals; Bibliography; Index.

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Book SynopsisThis book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the CoxâRossâRubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems.Trade Review'The book could be used by a broad range of practitioners, such as analysts, risk managers, quants, consultants, and auditors in financial markets, as it provides an overview of all the basic terminologies and concepts of financial models.' Thomas S. Y. Ho, SIAM Review'… clearly written … The exposition is of well-known material, using the classical notation, and plenty of exercises for the reader are integrated into the text.' George Matthews, Mathematics TodayTable of ContentsPreface; 1. Introduction; 2. Single-step asset pricing models; 3. Multi-step binomial model; 4. Multi-step general models; 5. American options; 6. Modelling bonds and interest rates; Index.

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Book SynopsisStudents and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.Table of ContentsPreface; 1. Probability space; 2. Probability distributions and random variables; 3. Product measure and independence; 4. Conditional expectation; 5. Sequences of random variables; Index.

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Book SynopsisWith its emphasis on examples, exercises and calculations, this book suits advanced undergraduates as well as postgraduates and practitioners. It provides a clear treatment of the scope and limitations of mean-variance portfolio theory and introduces popular modern risk measures. Proofs are given in detail, assuming only modest mathematical background, but with attention to clarity and rigour. The discussion of VaR and its more robust generalizations, such as AVaR, brings recent developments in risk measures within range of some undergraduate courses and includes a novel discussion of reducing VaR and AVaR by means of hedging techniques. A moderate pace, careful motivation and more than 70 exercises give students confidence in handling risk assessments in modern finance. Solutions and additional materials for instructors are available at www.cambridge.org/9781107003675.Table of ContentsPreface; 1. Risk and return; 2. Portfolios consisting of two assets; 3. Lagrange multipliers; 4. Portfolios of multiple assets; 5. The capital asset pricing model; 6. Utility functions; 7. Value at risk; 8. Coherent measures of risk; Index.

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Book SynopsisThe BlackâScholes option pricing model is the first and by far the best-known continuous-time mathematical model used in mathematical finance. Here, it provides a sufficiently complex, yet tractable, testbed for exploring the basic methodology of option pricing. The discussion of extended markets, the careful attention paid to the requirements for admissible trading strategies, the development of pricing formulae for many widely traded instruments and the additional complications offered by multi-stock models will appeal to a wide class of instructors. Students, practitioners and researchers alike will benefit from the book's rigorous, but unfussy, approach to technical issues. It highlights potential pitfalls, gives clear motivation for results and techniques and includes carefully chosen examples and exercises, all of which make it suitable for self-study.Table of ContentsPreface; 1. Introduction; 2. Strategies and risk-neutral probability; 3. Option pricing and hedging; 4. Various extensions and applications; 5. Path-dependent options; 6. General models; Index.

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Book SynopsisStudents and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.Table of ContentsPreface; 1. Probability space; 2. Probability distributions and random variables; 3. Product measure and independence; 4. Conditional expectation; 5. Sequences of random variables; Index.

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Book SynopsisThis book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Ità integrals in some detail, with a focus on results needed for the BlackâScholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Ità formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Ità calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.Trade Review'… a very accessible and comprehensive introduction.' Robert Stelzer, Mathematical ReviewsTable of ContentsPreface; 1. Discrete time processes; 2. Wiener process; 3. Stochastic integrals; 4. Itô formula; 5. Stochastic differential equations; Index.

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