Chin / Ólafsson / Nel Problems and Solutions in Mathematical Finance

Stochastic Calculus, Volume I
1. Auflage 2014
ISBN: 978-1-119-96608-1
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 1, 400 Seiten, E-Book

Reihe: Wiley Finance Series

Mathematical finance requires the use of advanced mathematicaltechniques drawn from the theory of probability, stochasticprocesses and stochastic differential equations. These areas aregenerally introduced and developed at an abstract level, making itproblematic when applying these techniques to practical issues infinance.
Problems and Solutions in Mathematical Finance Volume I:Stochastic Calculus is the first of a four-volume set ofbooks focusing on problems and solutions in mathematicalfinance.
This volume introduces the reader to the basic stochasticcalculus concepts required for the study of this important subject,providing a large number of worked examples which enable the readerto build the necessary foundation for more practical orientatedproblems in the later volumes. Through this application and byworking through the numerous examples, the reader will properlyunderstand and appreciate the fundamentals that underpinmathematical finance.
Written mainly for students, industry practitioners and thoseinvolved in teaching in this field of study, StochasticCalculus provides a valuable reference book to complementone's further understanding of mathematical finance.

Autoren/Hrsg.

Ólafsson, Sverrir

Nel, Dian

Inhaltsverzeichnis

1. General Probability and Statistical Theory
1.1 Introduction
1.2 Problems and Solutions
1.2.1 Probability Spaces
1.2.2 Discrete and Continuous Random Variables
1.2.3 Properties of Expectations
2. General Statistical Theory
2.1 Introduction
2.2 Problems and Solutions
2.2.1 Parameter Estimation
2.2.2 Hypotheses Testing
2.2.3 Goodness of Fit Analysis
2.2.4 Regression Analysis
3. Wiener Process
3.1 Introduction
3.2 Problems and Solutions
3.2.1  Random Walks
3.2.2 Examples of Wiener Process
3.2.3 Markov Property
3.2.4 Martingale Property
3.2.5 First Passage Time
3.2.6 Reflection Principle
3.2.7 Quadratic Variation
4. Stochastic Differential Equations
4.1 Introduction
4.2 Problems and Solutions
4.2.1 Ito Calculus
4.2.2 One-Dimension Diffusion Process
4.2.3 Multi-Dimensional Diffusion Process
5. Change of Measure
5.1 Introduction
5.2 Problems and Solutions
5.2.1 Martingale Representation Theorem
5.2.2 Girsanov's Theorem
5.2.3 Risk Neutral Measure
6. Poisson Process
6.1 Introduction
6.2 Problems and Solutions
6.2.1 Properties of Poisson Process
6.2.2 Jump Diffusion Process
6.2.3 Change of Measure
Appendix A Mathematics Formulae
Appendix B Probability Theory Formulae
Appendix C Statistical Theory Formulae
Appendix D Differential Equations Formulae

Über Autor(innen)

Eric Chin is a quantitative analyst at an investment bankin the City of London where he is involved in providing guidance onprice testing methodologies and their implementation, formulatingmodel calibration and model appropriateness on commodity and creditproducts. Prior to joining the banking industry he worked as asenior researcher at British Telecom investigating radio spectrumtrading and risk management within the telecommunications sector.Eric Chin holds an MSc in Applied Statistics and an MSc inMathematical Finance both from University of Oxford. He also holdsa PhD in Mathematics from University of Dundee.
Dian Nel has more than 10 years of experience in thecommodities sector. He currently works in the City of London wherehe specialises in oil and gas markets. He holds a BEng inElectrical and Electronic Engineering from StellenboschUniversityand an MSc in Mathematical Finance from ChristChurch,OxfordUniversity. He is a Chartered Engineer registered with theEngineering Council UK.
Sverrir Olafsson is Professor of Financial Mathematics atReykjavik University; a Visiting Professor at QueenMaryUniversity,London and a director of Riskcon Ltd, a UK based risk managementconsultancy. Previously he was a Chief Researcher at BT Researchand held academic positions at The Mathematical Departments ofKings College, London; UMIST Manchester and The University ofSouthampton. Dr Olafsson is the author of over 95 refereed academicpapers and has been a key note speaker at numerous internationalconferences and seminars. He is on the editorial board of threeinternational journals. He has provided an extensive consultancy onfinancial risk management and given numerous specialist seminars tofinance specialists. In the last five years his main teaching hasbeen MSc courses on Risk Management, Fixed Income, and MathematicalFinance.
Dr Olafsson has an MSc and PhD in mathematical physics from theUniversities of Tübingen and Karlsruhe respectively.