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

Lutz Kruschwitz is professor emeritus at the chair of banking and finance, the Free University of Berlin. He graduated in economics from this university. His research interests include investment and valuation theory. He is the author of several bestselling German finance textbooks. He received an honorary doctorate from the University of Tuebingen and is an honorary professor at the University of Vienna. Andreas Löffler studied Mathematics at the Leipzig University and the Academy of Science in Berlin. He obtained his Ph.D. in Mathematics in 1993 and a second Ph.D. in Economics in 1995 from the University of Leipzig . From 2000 he is a tenured professor at the chair of banking and finance at the University of Hannover. Since 2006 he is the chair of banking and finance at Friedrich Alexander University, Erlangen-Nuremberg. In 2008 he moved to Paderborn as a professor of finance and investment. Since 2011 he holds the chair of finance at the Free University of Berlin.

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