Introductory Mathematical Analysis for Quantitative Finance

This textbook is designed to enable students with little knowledge of mathematical analysis to engage with modern quantitative finance. The exposition of the topics is concise as chapters are intended to represent a preliminary contact with the mathematical concepts used in QF.

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.

  Autorentext

Daniele Ritelli is associate professor of mathematical analysis at the Department of Statistical Sciences of the University of Bologna, in Italy. He teaches ordinary and partial differential equations and special functions in various three-year and magister degree courses in statistics and finance. His research interests concern special functions, ordinary differential equations and pure and applied mathematics.

Giulia Spaletta is associate professor of numerical analysis at the Department of Statistical Sciences of the University of Bologna, in Italy. She lectures in various three-year and master degree courses in computer science, statistics and economics. Her research interests include numerical error analysis in linear algebra and differential equations and numerical modeling in biomedical engineering.

Klappentext

This textbook is designed to enable students with little knowledge of mathematical analysis to engage with modern quantitative finance. The exposition of the topics is concise as chapters are intended to represent a preliminary contact with the mathematical concepts used in QF.

Inhalt

Euclidean space. Sequences and series of functions. Multidimensional differential calculus. Ordinary differential equations of first order: methods for explicit solutions. Linear differential equations of second order. Prologue to Measure theory. Lebesgue integral. Radon-Nikodym theorem. Multiple integrals. Gamma and Beta functions. Fourier ransform on the real line. Parabolic equations.