Financial Calculus

Author: Martin Baxter
Publisher: Cambridge University Press
ISBN: 9780521552899
Format: PDF, ePub
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A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

A Course in Financial Calculus

Author: Alison Etheridge
Publisher: Cambridge University Press
ISBN: 9780521890779
Format: PDF, Kindle
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A text for first courses in financial calculus; lots of examples and exercises, first published in 2002.

Financial Calculus in MATLAB Cvar and Mad Portfolios Optimization

Author: J. Perkins
Publisher: Createspace Independent Publishing Platform
ISBN: 9781983487255
Format: PDF, Kindle
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Portfolio optimization problems involve identifying portfolios that satisfy three criteria: Minimize a proxy for risk, Match or exceed a proxy for return and Satisfy basic feasibility requirements. Portfolios are points from a feasible set of assets that constitute an asset universe. A portfolio specifies either holdings or weights in each individual asset in the asset universe. The convention is to specify portfolios in terms of weights, although the portfolio optimization tools work with holdings as well. The set of feasible portfolios is necessarily a nonempty, closed, and bounded set. The proxy for risk is a function that characterizes either the variability or losses associated with portfolio choices. The proxy for return is a function that characterizes either the gross or net benefits associated with portfolio choices. The terms "risk" and "risk proxy" and "return" and "return proxy" are interchangeable. The fundamental insight of Markowitz is that the goal of the portfolio choice problem is to seek minimum risk for a given level of return and to seek maximum return for a given level of risk. Portfolios satisfying these criteria are efficient portfolios and the graph of the risks and returns of these portfolios forms a curve called the efficient frontier. Financial Toolbox has three objects to solve specific types of portfolio optimization problems: - The Portfolio object (Portfolio) supports mean-variance portfolio optimization. This object has either gross or net portfolio returns as the return proxy, the variance of portfolio returns as the risk proxy, and a portfolio set that is any combination of the specified constraints to form a portfolio set. - The Portfolio CVaR object (PortfolioCVaR) implements what is known as conditional value-at-risk portfolio optimization, which is generally referred to as CVaR portfolio optimization. CVaR portfolio optimization works with the same return proxies and portfolio sets as mean-variance portfolio optimization but uses conditional value-at-risk of portfolio returns as the risk proxy. - The Portfolio MAD object (PortfolioMAD) implements what is known as meanabsolute deviation portfolio optimization, which is referred to as MAD portfolio optimization. MAD portfolio optimization works with the same return proxies and portfolio sets as mean-variance portfolio optimization but uses mean-absolute deviation portfolio returns as the risk proxy.

Elementary Stochastic Calculus with Finance in View

Author: Thomas Mikosch
Publisher: World Scientific
ISBN: 9789810235437
Format: PDF
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Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

Stochastic Calculus for Finance I

Author: Steven Shreve
Publisher: Springer Science & Business Media
ISBN: 0387225277
Format: PDF, Docs
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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.

Islamic Finance

Author: Mahmoud A. El-Gamal
Publisher: Cambridge University Press
ISBN: 1139457160
Format: PDF, ePub
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This book provides an overview of the practice of Islamic finance and the historical roots that define its modes of operation. The focus of the book is analytical and forward-looking. It shows that Islamic finance exists mainly as a form of rent-seeking legal-arbitrage. In every aspect of finance - from personal loans to investment banking, and from market structure to corporate governance - Islamic finance aims to replicate in Islamic forms the substantive functions of contemporary financial instruments, markets, and institutions. By attempting to replicate the substance of contemporary financial practice using pre-modern contract forms, Islamic finance has arguably failed to serve the objectives of Islamic law. This book proposes refocusing Islamic finance on substance rather than form. This approach would entail abandoning the paradigm of 'Islamization' of every financial practice. It would also entail reorienting the brand-name of Islamic finance to emphasize issues of community banking, micro-finance, and socially responsible investment.

Stochastic Calculus and Financial Applications

Author: J. Michael Steele
Publisher: Springer Science & Business Media
ISBN: 1468493051
Format: PDF, ePub
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Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH

Stochastic Calculus for Finance II

Author: Steven E. Shreve
Publisher: Springer Science & Business Media
ISBN: 9780387401010
Format: PDF, Mobi
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This is the second volume in a two-volume sequence on Stochastic calculus models in finance. This second volume, which does not require the first volume as a prerequisite, covers infinite state models and continuous time stochastic calculus. The book is suitable for beginning masters-level students in mathematical finance and financial engineering.

Telegraph Processes and Option Pricing

Author: Alexander D. Kolesnik
Publisher: Springer Science & Business Media
ISBN: 3642405266
Format: PDF, Docs
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The telegraph process is a useful mathematical model for describing the stochastic motion of a particle that moves with finite speed on the real line and alternates between two possible directions of motion at random time instants. That is why it can be considered as the finite-velocity counterpart of the classical Einstein-Smoluchowski's model of the Brownian motion in which the infinite speed of motion and the infinite intensity of the alternating directions are assumed. The book will be interesting to specialists in the area of diffusion processes with finite speed of propagation and in financial modelling. It will also be useful for students and postgraduates who are taking their first steps in these intriguing and attractive fields.

Elementary Calculus of Financial Mathematics

Author: A. J. Roberts
Publisher: SIAM
ISBN: 9780898718225
Format: PDF, ePub
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Financial mathematics and its calculus introduced in an accessible manner for undergraduate students. Topics covered include financial indices as stochastic processes, Ito's stochastic calculus, the Fokker-Planck Equation and extra MATLAB/SCILAB code.