The Brownian Motion : : A Rigorous but Gentle Introduction for Economists.

• Superior document: Springer Texts in Business and Economics Series
• Author: Löffler, Andreas.
• TeilnehmendeR: Kruschwitz, Lutz.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2019.; {copy}2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Series: Springer Texts in Business and Economics Series
• Physical Description: 1 online resource (130 pages)

Table of Contents

• Intro
• Preface
• Acknowledgments
• Contents
• 1 Introduction
• 1.1 Stochastics in Finance Theory
• 1.2 Precision and Intuition in the Valuation of Derivatives
• 1.3 Purpose of the Book
• 2 Set Theory
• 2.1 Notation and Set Operations
• 2.2 Events and Sets
• 3 Measures and Probabilities
• 3.1 Basic Problem of Measurement Theory
• 3.2 σ-Algebras and Their Formal Definition
• 3.3 Examples of Measurable Sets and Their Interpretation
• 3.4 Further Examples: Infinite Number of States and Times
• 3.5 Definition of a Measure
• 3.6 Stieltjes Measure
• 3.7 Dirac Measure
• 3.8 Null Sets and the Almost-Everywhere Property
• 4 Random Variables
• 4.1 Random Variables as Functions
• 4.2 Random Variables as Measurable Functions
• 4.3 Distribution Functions
• 5 Expectation and Lebesgue Integral
• 5.1 Definition of Expectation: A Problem
• 5.2 Riemann Integral
• 5.3 Lebesgue Integral
• 5.4 Result: Expectation and Variance as Lebesgue Integral
• 5.5 Conditional Expectation
• 6 Wiener's Construction of the Brownian Motion
• 6.1 Preliminary Remark: The Space of All Paths
• 6.2 Wiener Measure on the Space of Continuous Functions
• 6.3 Two Definitions of the Brownian Motion
• 6.4 Often Neglected Properties of the Brownian Motion
• 7 Supplements
• 7.1 Cardinality of Sets
• 7.2 Continuous and Almost Nowhere Differentiable Functions
• 7.3 Convergence Terms
• 7.4 Conditional Expectations Are Random Variables
• References
• Index.