The Brownian Motion : A Rigorous but Gentle Introduction for Economists.
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| Other Authors: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing AG,
2019.
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| Edition: | 1st ed. |
| Series: | Springer Texts in Business and Economics Series
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| Subjects: | |
| Online Access: | Click to View |
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.