| Title Details: | |
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Introduction to Stochastic Calculus |
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| Authors: |
Cheliotis, Dimitrios |
| Reviewer: |
Loulakis, Michail |
| Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > STOCHASTIC ANALYSIS MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > STOCHASTIC PROCESSES |
| Keywords: |
Brownian Motion
Martingales Financial Mathematics Conditional Expectation Stochastic Integral Itô Calculus |
| Description: | |
| Abstract: |
The book is intended for advanced undergaduate students in Mathematics departments and covers the following material. a) Conditional expectation, martingales in discrete time (basic properties and applications). b) Brownian motion: Construction, simple properties, strong Markov property, analytical properties, Brownian martingales. c) Construction of the Itô integral and Itô’s formula. d) Stochastic differential equations. e) Elements of Financial Mathematics, Pricing of European derivatives, Black-Scholes equation.
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| Linguistic Editors: |
Trampoulis, Τheofilos |
| Type: |
Undergraduate textbook |
| Creation Date: | 2015 |
| Item Details: | |
| ISBN |
978-960-603-297-4 |
| License: |
http://creativecommons.org/licenses/by-nc-nd/3.0/gr |
| DOI | http://dx.doi.org/10.57713/kallipos-605 |
| Handle | http://hdl.handle.net/11419/4143 |
| Bibliographic Reference: | Cheliotis, D. (2015). Introduction to Stochastic Calculus [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-605 |
| Language: |
Greek |
| Consists of: |
1. Introduction 2. Conditional expectation 3. Martingales 4. Processes in continuous time 5. Construction of Brownian motion and simple properties 6. Strong Markov property and implication 7. Martingales and Brownian motion 8. Analytical properties 9. Construction of the integral 10. The integral as a process 11. Extensions of the integral 12. Itô formula 13. Applications to Brownian motion 14. Stochastic differential equations 15. Solution of special SDEs 16. Portfolios and arbitrage 17. European options 18. Black-Scholes equation |
| Number of pages |
173 |
| Publication Origin: |
Kallipos, Open Academic Editions |
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