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Risk neutral pricing and financial mathematics : a primer /
Risk Neutral Pricing and Financial Mathematics: A Primer provides a foundation to financial mathematics for those whose undergraduate quantitative preparation does not extend beyond calculus, statistics, and linear math. It covers a broad range of foundation topics related to financial modeling, inc...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Diego, CA :
Academic Press, an imprint of Elsevier,
2015.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Risk Neutral Pricing and Financial Mathematics; Copyright Page; Dedication; Contents; About the Authors; Preface; 1 Preliminaries and Review; 1.1 Financial Models; 1.2 Financial Securities and Instruments; 1.3 Review of Matrices and Matrix Arithmetic; 1.3.1 Matrix Arithmetic; 1.3.1.1 Matrix Arithmetic Properties; 1.3.1.2 The Inverse Matrix; Illustration: The Gauss-Jordan Method; Illustration: Solving Systems of Equations; 1.3.2 Vector Spaces, Spanning, and Linear Dependence; 1.3.2.1 Linear Dependence and Linear Independence; Illustrations: Linear Dependence and Independence.
- 1.3.2.2 Spanning the Vector Space and the BasisIllustration: Spanning the Vector Space and the Basis; 1.4 Review of Differential Calculus; 1.4.1 Essential Rules for Calculating Derivatives; 1.4.1.1 The Power Rule; 1.4.1.2 The Sum Rule; 1.4.1.3 The Chain Rule; 1.4.1.4 Product and Quotient Rules; 1.4.1.5 Exponential and Log Function Rules; 1.4.2 The Differential; Illustration: The Differential and the Error; 1.4.3 Partial Derivatives; 1.4.3.1 The Chain Rule for Two Independent Variables; 1.4.4 Taylor Polynomials and Expansions; 1.4.5 Optimization and the Method of Lagrange Multipliers.
- Illustration: Lagrange Optimization1.5 Review of Integral Calculus; 1.5.1 Antiderivatives; 1.5.2 Definite Integrals; 1.5.2.1 Reimann Sums; 1.5.3 Change of Variables Technique to Evaluate Integrals; Illustration: Change of Variables Technique for the Indefinite Integral; 1.5.3.1 Change of Variables Technique for the Definite Integral; 1.6 Exercises; Notes; 2 Probability and Risk; 2.1 Uncertainty in Finance; 2.2 Sets and Measures; 2.2.1 Sets; Illustration: Toss of Two Dice; 2.2.1.1 Finite, Countable, and Uncountable Sets; 2.2.2 Measurable Spaces and Measures; 2.3 Probability Spaces.
- 2.3.1 Physical and Risk-Neutral ProbabilitiesIllustration: Probability Space; 2.3.2 Random Variables; Illustration: Discrete Random Variables; 2.4 Statistics and Metrics; 2.4.1 Metrics in Discrete Spaces; 2.4.1.1 Expected Value, Variance, and Standard Deviation; Illustration; 2.4.1.2 Co-movement Statistics; 2.4.2 Metrics in Continuous Spaces; Illustration: Distributions in a Continuous Space; 2.4.2.1 Expected Value and Variance; 2.5 Conditional Probability; Illustration: Drawing a Spade; 2.5.1 Bayes Theorem; Illustration: Detecting Illegal Insider Trading; 2.5.2 Independent Random Variables.
- Illustration2.5.2.1 Multiple Random Variables; 2.6 Distributions and Probability Density Functions; 2.6.1 The Binomial Random Variable; Illustration: Coin Tossing; Illustration: DK Trades; 2.6.2 The Uniform Random Variable; Illustration: Uniform Random Variable; 2.6.3 The Normal Random Variable; 2.6.3.1 Calculating Cumulative Normal Density; 2.6.3.2 Linear Combinations of Independent Normal Random Variables; 2.6.4 The Lognormal Random Variable; 2.6.4.1 The Expected Value of the Lognormal Distribution; Illustration: Risky Securities; 2.6.5 The Poisson Random Variable.