ABSTRACT

Introductory Mathematical Analysis for Quantitative Finance is a textbook designed to enable students with little knowledge of mathematical analysis to fully engage with modern quantitative finance. A basic understanding of dimensional Calculus and Linear Algebra is assumed.

The exposition of the topics is as concise as possible, since the chapters are intended to represent a preliminary contact with the mathematical concepts used in Quantitative Finance. The aim is that this book can be used as a basis for an intensive one-semester course.

Features:

  • Written with applications in mind, and maintaining mathematical rigor.
  • Suitable for undergraduate or master's level students with an Economics or Management background.
  • Complemented with various solved examples and exercises, to support the understanding of the subject.

chapter Chapter 1|12 pages

Euclidean space

chapter Chapter 2|43 pages

Sequences and series of functions

chapter Chapter 3|15 pages

Multidimensional differential calculus

chapter Chapter 6|23 pages

Linear differential equations of second order

chapter Chapter 7|10 pages

Prologue to Measure theory

chapter Chapter 8|44 pages

Lebesgue integral

chapter Chapter 9|6 pages

Radon–Nikodym theorem

chapter Chapter 10|22 pages

Multiple integrals

chapter Chapter 11|16 pages

Gamma and Beta functions

chapter Chapter 12|13 pages

Fourier transform on the real line

chapter Chapter 13|29 pages

Parabolic equations