Gushchin Stochastic Calculus for Quantitative Finance

1. Auflage 2015
ISBN: 978-0-08-100476-0
Verlag: Morgan Kaufmann
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 208 Seiten, Format (B × H): 152 mm x 229 mm

In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school.

This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations.



- Contains the most popular applications of the theory of stochastic integration
- Details necessary facts from probability and analysis which are not included in many standard university courses such as theorems on monotone classes and uniform integrability
- Written by experts in the field of modern mathematical finance

Zielgruppe

Graduate students and professors worldwide working in all subdisciplines of economics and finance

Autoren/Hrsg.

Gushchin, Alexander A

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik

Inhaltsverzeichnis

Chapter 1. General theory of stochastic processes
Chapter 2. Martingales and processes with finite variation
Chapter 3. Stochastic integrals

Leseproben

List of Statements
Definitions
Definition 1.1 1 Definition 1.2 2 Definition 1.3 4 Definition 1.4 4 Definition 1.5 5 Definition 1.6 6 Definition 1.7 8 Definition 1.8 11 Definition 1.9 12 Definition 1.10 12 Definition 1.11 14 Definition 1.12 15 Definition 1.13 17 Definition 1.14 17 Definition 1.15 22 Definition 1.16 27 Definition 1.17 30 Definition 1.18 30 Definition 2.1 41 Definition 2.2 42 Definition 2.3 42 Definition 2.4 44 Definition 2.5 46 Definition 2.6 52 Definition 2.7 53 Definition 2.8 62 Definition 2.9 64 Definition 2.10 67 Definition 2.11 68 Definition 2.12 68 Definition 2.13 69 Definition 2.14 74 Definition 2.15 79 Definition 2.16 83 Definition 2.17 98 Definition 2.18 99 Definition 2.19 101 Definition 2.20 101 Definition 2.21 107 Definition 2.22 108 Definition 2.23 112 Definition 2.24 113 Definition 2.25 116 Definition 3.1 124 Definition 3.2 129 Definition 3.3 131 Definition 3.4 136 Definition 3.5 136 Definition 3.6 140 Definition 3.7 140 Definition 3.8 141 Definition 3.9 156 Definition 3.10 162 Definition A.1 170 Definition A.2 171 Examples
Example 1.1 2 Example 1.2 5 Example 1.3 5 Example 2.1 57 Example 2.2 59 Example 2.3 86 Example 2.4 90 Example 2.5 102 Example 2.6 103 Example 2.7 103 Example 3.1 127 Example 3.2 135 Example 3.3 164 Exercises
Exercise 1.1 2 Exercise 1.2 2 Exercise 1.3 2 Exercise 1.4 3 Exercise 1.5 4 Exercise 1.6 5 Exercise 1.7 6 Exercise 1.8 6 Exercise 1.9 6 Exercise 1.10 8 Exercise 1.11 11 Exercise 1.12 12 Exercise 1.13 12 Exercise 1.14 15 Exercise 1.15 18 Exercise 1.16 22 Exercise 1.17 22 Exercise 1.18 24 Exercise 1.19 26 Exercise 1.20 26 Exercise 1.21 27 Exercise 1.22 27 Exercise 1.23 28 Exercise 1.24 28 Exercise 1.25 28 Exercise 1.26 30 Exercise 1.27 34 Exercise 1.28 34 Exercise 1.29 34 Exercise 1.30 34 Exercise 1.31 35 Exercise 1.32 35 Exercise 1.33 36 Exercise 1.34 36 Exercise 1.35 36 Exercise 1.36 37 Exercise 1.37 38 Exercise 1.38 39 Exercise 1.39 39 Exercise 1.40 39 Exercise 1.41 39 Exercise 2.1 41 Exercise 2.2 42 Exercise 2.3 42 Exercise 2.4 42 Exercise 2.5 43 Exercise 2.6 43 Exercise 2.7 43 Exercise 2.8 43 Exercise 2.9 43 Exercise 2.10 44 Exercise 2.11 45 Exercise 2.12 46 Exercise 2.13 47 Exercise 2.14 48 Exercise 2.15 49 Exercise 2.16 49 Exercise 2.17 59 Exercise 2.18 59 Exercise 2.19 59 Exercise 2.20 62 Exercise 2.21 63 Exercise 2.22 64 Exercise 2.23 67 Exercise 2.24 68 Exercise 2.25 68 Exercise 2.26 70 Exercise 2.27 73 Exercise 2.28 73 Exercise 2.29 74 Exercise 2.30 80 Exercise 2.31 80 Exercise 2.32 80 Exercise 2.33 81 Exercise 2.34 81 Exercise 2.35 81 Exercise 2.36 87 Exercise 2.37 91 Exercise 2.38 91 Exercise 2.39 91 Exercise 2.40 98 Exercise 2.41 99 Exercise 2.42 100 Exercise...