List of Tables.

List of Examples.

Foreword.

Preface to Volume 1.

I.1 Basic Calculus for Finance.

I.1.1 Introduction.

I.1.2 Functions and Graphs, Equations and Roots.

I.1.3 Differentiation and Integration.

I.1.4 Analysis of Financial Returns.

I.1.5 Functions of Several Variables.

I.1.6 Taylor Expansion.

I.1.7 Summary and Conclusions.

I.2 Essential Linear Algebra for Finance.

I.2.1 Introduction.

I.2.2 Matrix Algebra and its Mathematical Applications.

I.2.3 Eigenvectors and Eigenvalues.

I.2.4 Applications to Linear Portfolios.

I.2.5 Matrix Decomposition.

I.2.6 Principal Component Analysis.

I.2.7 Summary and Conclusions.

I.3 Probability and Statistics.

I.3.1 Introduction.

I.3.2 Basic Concepts.

I.3.3 Univariate Distributions.

I.3.4 Multivariate Distributions.

I.3.5 Introduction to Statistical Inference.

I.3.6 Maximum Likelihood Estimation.

I.3.7 Stochastic Processes in Discrete and Continuous Time.

I.3.8 Summary and Conclusions.

I.4 Introduction to Linear Regression.

I.4.1 Introduction.

I.4.2 Simple Linear Regression.

I.4.3 Properties of OLS Estimators.

I.4.4 Multivariate Linear Regression.

I.4.5 Autocorrelation and Heteroscedasticity.

I.4.6 Applications of Linear Regression in Finance.

I.4.7 Summary and Conclusions.

I.5 Numerical Methods in Finance.

I.5.1 Introduction.

I.5.2 Iteration.

I.5.3 Interpolation and Extrapolation.

I.5.4 Optimization.

I.5.5 Finite Difference Approximations.

I.5.6 Binomial Lattices.

I.5.7 Monte Carlo Simulation.

I.5.8 Summary and Conclusions.

I.6 Introduction to Portfolio Theory.

I.6.1 Introduction.

I.6.2 Utility Theory.

I.6.3 Portfolio Allocation.

I.6.4 Theory of Asset Pricing.

I.6.5 Risk Adjusted Performance Measures.

I.6.6 Summary and Conclusions.

References.

Statistical Tables.

Index.