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Introduction to Quantitative Finance A Math

ISBN-10: 026201369X

ISBN-13: 9780262013697

Edition: 2010

Authors: Robert R. Reitano

List price: $85.00
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Description:

This text offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems. It emphasizes the thought process and mathematical approach taken to develop each result instead of the memorization of formulas to be applied (or misapplied) automatically. The objective is to provide a deep level of understanding of the relevant mathematical theory and tools that can then be effectively used in practice, to teach students how to "think in mathematics" rather than simply to do mathematics by rote. Each chapter covers an area of mathematics such as mathematical logic, Euclidean and other spaces, set theory and topology, sequences and series, probability theory, and calculus, in each case presenting only material that is most important and relevant for quantitative finance. Each chapter includes finance applications that demonstrate the relevance of the material presented. Problem sets are offered on both the mathematical theory and the finance applications sections of each chapter. The logical organization of the book and the judicious selection of topics make the text customizable for a number of courses. The development is self-contained and carefully explained to support disciplined independent study as well. A solutions manual for students provides solutions to the book's Practice Exercises; an instructor's manual offers solutions to the Assignment Exercises as well as other materials.
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Book details

List price: $85.00
Copyright year: 2010
Publisher: MIT Press
Publication date: 1/29/2010
Binding: Hardcover
Pages: 736
Size: 7.25" wide x 9.50" long x 1.50" tall
Weight: 2.530
Language: English

Robert R. Reitano is Professor of the Practice in Finance at Brandeis University's International Business School. He was formerly Executive Vice President and Chief Investment Strategist of John Hancock/Manulife.

Complete Table of Contents
List of Figures and Tables
Introduction
Mathematical Logic
Introduction
Axiomatic Theory
Inferences
Paradoxes
Propositional Logic
Mathematical Logic
Applications to Finance
Exercises
Number Systems and Functions
Numbers: Properties and Structures
Functions
Applications to Finance
Exercises
Euclidean and Other Spaces
Euclidean Space
Metric Spaces
Applications to Finance
Exercises
Set Theory and Topology
Set Theory
Open, Closed, and Other Sets
Applications to Finance
Exercises
Sequences and Their Convergence
Numerical Sequences
Limits Superior and Inferior
General Metric Space Sequences
Cauchy Sequences
Applications to Finance
Exercises
Series and Their Convergence
Numerical Series
The lp-Spaces
Power Series
Applications to Finance
Exercises
Discrete Probability Theory
The Notion of Randomness
Sample Spaces
Combinatorics
Random Variables
Expectations of Discrete Distributions
Discrete Probability Density Functions
Generating Random Samples
Applications to Finance
Exercises
Fundamental Probability Theorems
Uniqueness of the m.g.f. and c.f.
Chebyshev's Inequality
Weak Law of Large Numbers
Strong Law of Large Numbers
De Moivre-Laplace Theorem
The Normal Distribution
The Central Limit Theorem
Applications to Finance
Exercises
Calculus I: Differentiation
Approximating Smooth Functions
Functions and Continuity
Derivatives and Taylor Series
Convergence of a Sequence of Derivatives
Critical Point Analysis
Concave and Convex Functions
Approximating Derivatives
Applications to Finance
Exercises
Calculus II: Integration
Summing Smooth Functions
Riemann Integration of Functions
Examples of the Riemann Integral
Mean Value Theorem for Integrals
Integrals and Derivatives
Improper Integrals
Formulaic Integration Tricks
Taylor Series with Integral Remainder
Convergence of a Sequence of Integrals
Numerical Integration
Continuous Probability Theory
Applications to Finance
Exercises
References
Index