Produktbild: Mathematical Methods for Finance

Mathematical Methods for Finance

Aus der Reihe Frank J. Fabozzi Series

149,99 €

inkl. gesetzl. MwSt., Versandkostenfrei


Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

23.09.2013

Verlag

John Wiley & Sons

Seitenzahl

320

Maße (L/B/H)

23,1/15,2/3,3 cm

Gewicht

522 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-31263-6

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

23.09.2013

Verlag

John Wiley & Sons

Seitenzahl

320

Maße (L/B/H)

23,1/15,2/3,3 cm

Gewicht

522 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-118-31263-6

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: GPSR Kontakt

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  • Produktbild: Mathematical Methods for Finance
  • Preface xi
     
    About the Authors xvii
     
    CHAPTER 1 Basic Concepts: Sets, Functions, and Variables 1
     
    Introduction 2
     
    Sets and Set Operations 2
     
    Distances and Quantities 6
     
    Functions 10
     
    Variables 10
     
    Key Points 11
     
    CHAPTER 2 Differential Calculus 13
     
    Introduction 14
     
    Limits 15
     
    Continuity 17
     
    Total Variation 19
     
    The Notion of Differentiation 19
     
    Commonly Used Rules for Computing Derivatives 21
     
    Higher-Order Derivatives 26
     
    Taylor Series Expansion 34
     
    Calculus in More Than One Variable 40
     
    Key Points 41
     
    CHAPTER 3 Integral Calculus 43
     
    Introduction 44
     
    Riemann Integrals 44
     
    Lebesgue-Stieltjes Integrals 47
     
    Indefinite and Improper Integrals 48
     
    The Fundamental Theorem of Calculus 51
     
    Integral Transforms 52
     
    Calculus in More Than One Variable 57
     
    Key Points 57
     
    CHAPTER 4 Matrix Algebra 59
     
    Introduction 60
     
    Vectors and Matrices Defined 61
     
    Square Matrices 63
     
    Determinants 66
     
    Systems of Linear Equations 68
     
    Linear Independence and Rank 69
     
    Hankel Matrix 70
     
    Vector and Matrix Operations 72
     
    Finance Application 78
     
    Eigenvalues and Eigenvectors 81
     
    Diagonalization and Similarity 82
     
    Singular Value Decomposition 83
     
    Key Points 83
     
    CHAPTER 5 Probability: Basic Concepts 85
     
    Introduction 86
     
    Representing Uncertainty with Mathematics 87
     
    Probability in a Nutshell 89
     
    Outcomes and Events 91
     
    Probability 92
     
    Measure 93
     
    Random Variables 93
     
    Integrals 94
     
    Distributions and Distribution Functions 96
     
    Random Vectors 97
     
    Stochastic Processes 100
     
    Probabilistic Representation of Financial Markets 102
     
    Information Structures 103
     
    Filtration 104
     
    Key Points 106
     
    CHAPTER 6 Probability: Random Variables and Expectations 107
     
    Introduction 109
     
    Conditional Probability and Conditional Expectation 110
     
    Moments and Correlation 112
     
    Copula Functions 114
     
    Sequences of Random Variables 116
     
    Independent and Identically Distributed Sequences 117
     
    Sum of Variables 118
     
    Gaussian Variables 120
     
    Appproximating the Tails of a Probability Distribution: Cornish-Fisher Expansion and Hermite Polynomials 123
     
    The Regression Function 129
     
    Fat Tails and Stable Laws 131
     
    Key Points 144
     
    CHAPTER 7 Optimization 147
     
    Introduction 148
     
    Maxima and Minima 149
     
    Lagrange Multipliers 151
     
    Numerical Algorithms 156
     
    Calculus of Variations and Optimal Control Theory 161
     
    Stochastic Programming 163
     
    Application to Bond Portfolio: Liability-Funding Strategies 164
     
    Key Points 178
     
    CHAPTER 8 Difference Equations 181
     
    Introduction 182
     
    The Lag Operator L 183
     
    Homogeneous Difference Equations 183
     
    Recursive Calculation of Values of Difference Equations 192
     
    Nonhomogeneous Difference Equations 195
     
    Systems of Linear Difference Equations 201
     
    Systems of Homogeneous Linear Difference Equations 202
     
    Key Points 209
     
    CHAPTER 9 Differential Equations 211
     
    Introduction 212
     
    Differential Equations Defined 213
     
    Ordinary Differential Equations 213
     
    Systems of Ordinary Differential Equations 216
    &