The Brownian Motion

This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them accessible for readers with little or no previous knowledge of the field. It also includes mathematical definitions and the hidden stories behind the terms discussing why the theories are presented in specific ways.

Explains the mathematical background of modern financial theory Provides numerous illustrative examples that can be understood with basic mathematical knowledge Focusses on the practice by abstaining from elaborating proofs

Autorentext

Andreas Löffler received his postdoctoral qualification (habilitation) in Mathematics and Economics from the University of Leipzig and Free University Berlin, Germany, and has been a Professor of Banking and Finance at the Department of Finance, Accounting and Taxation of the Free University of Berlin since 2012.

Lutz Kruschwitz is a Professor Emeritus of Banking and Finance at the Free University of Berlin, Germany.

Zusammenfassung
"The textbook is excellent for economists and financial economists who want to understand a little deeper in the Brownian motion with this soft introduction." (Weiping Li, zbMATH 1426.91005, 2020)

Inhalt
Introduction.- Set Theory.- Measures and Probabilities.- Random Variables.- Expectation and Lebesque Integral.- Wiener's Construction of the Brownian motion.- Supplements.- References.- Index.