Introduction to Actuarial and Financial Mathematical Methods book cover

Introduction to Actuarial and Financial Mathematical Methods

This self-contained module for independent study covers the subjects most often needed by non-mathematics graduates, such as fundamental calculus, linear algebra, probability, and basic numerical methods. The easily-understandable text of Mathematical Methods for Actuarial and Financial Self-Study features examples, motivations, and lots of practice from a large number of end-of-chapter questions. Questions range from short calculations to large project-based assignments, all designed to promote independent thinking and the application of mathematical ideas. Model solutions are included.

The intuitive organization of Mathematical Methods for Actuarial and Financial Self-Study maximizes its usefulness as a means of self-study and as a reference source. Financial concepts and terminology introduce every mathematical concept and theory. For readers with diverse backgrounds entering programs of the Institute and Faculty of Actuaries, the Society of Actuaries, and the CFA Institute, Mathematical Methods for Actuarial and Financial Self-Study can provide a consistency of mathematical knowledge from the outset.

Audience
Actuarial and finance students worldwide who need to learn or revisit fundamental applied mathematical tools and techniques

Hardbound, 496 Pages

Published: July 2015

Imprint: Academic Press

ISBN: 978-0-12-800156-1

Contents

  • Part 1: Fundamental mathematics (a refresher)

    1. Permutations and combinations
    2. Functions
      1. Definition, notation and motivation
      2. Polynomials
      3. Logarithmic and exponential
      4. Trigonometric

    3. Inequalities
    4. Sequences and series
    5. Limits
    6. Differentiation
      1. Theory, notation and motivation
      2. Of common functions
      3. Product, quotient and function of a function rule
      4. Turning points
      5. Taylor’s theorem

    7. Integration
      1. Theory, notation and motivation
      2. Of common functions
      3. Methods of substitution and by parts
      4. Areas under curves

    8. Complex numbers
      1. Definition, notation and motivation
      2. Complex plane and polar form
      3. Conjugation
      4. Addition, subtraction, multiplication and division
      5. de Moivre’s formula

      Part 2: Further calculus

    9. Fundamental Theorem of Calculus
      1. Statement
      2. Usage

    10. Higher order derivatives
    11. Lagrange multipliers
    12. Piecewise functions
    13. Calculus of two (or more) variables
      1. Maxima and minima of functions with two (or more) variables
      2. Double (or higher) integrals

    14. Differential equations
      1. Definitions and motivations (ODE, PDE, linear, nonlinear)
      2. Solution of ODEs (exact, integrating factors, separable, linear)

      Part 3: Linear algebra

    15. Matrices, matrix addition and multiplication
    16. Determinants and inverses
    17. Application to systems of linear equations
    18. Linear difference equations
    19. Part 4: Probability

    20. Definition, notation and motivation

      1. Sample spaces
      2. Events
      3. Probability of an event
      4. Basic rules

    1. Conditional probability
      1. Independent and dependent events
      2. Bayes Theorem

    2. Random variables and distributions
      1. Discrete and continuous
      2. Moments
      3. Normal distribution
      4. Other single variable distributions (discrete and continuous)

    3. Multivariate distributions
    4. Part 5: Numerical methods

    5. Numerical differentiation and integration
      1. General strategies
      2. Errors
      3. Standard approaches

    6. Iterative techniques for root finding
      1. Bisection method
      2. Newton’s method
      3. Secant method
      4. Regula Falsi method
      5. Interpolation

    7. Random number generation in modelling
      1. Standard calculator and Excel functions
      2. Inverse-transform method
      3. Box-Muller method
      4. Polar method

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