Students and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory. Consequently it provides essential prerequisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes. Results are proved carefully and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises and worked examples that are integral to the text.
About the Author
Ekkehard Kopp is Emeritus Professor of Mathematics at the University of Hull, where he taught courses at all levels in analysis, measure and probability, stochastic processes and mathematical finance between 1970 and 2007. His editorial experience includes service as founding member of the Springer Finance series (1998–2008) and the Cambridge University Press AIMS Library Series. He has taught in the UK, Canada and South Africa and he has authored more than 50 research publications and five books.
Jan Malczak has published over 20 research papers. He has taught courses in analysis, differential equations, measure and probability, and in the theory of stochastic differential processes, mainly at the Jagiellonian University in Kraków. He has supervised about 60 MSc dissertations, mostly in mathematical finance. He is now Professor of Mathematics in the Faculty of Applied Mathematics at AGH University of Science and Technology in Kraków, Poland.
Tomasz Zastawniak holds the Chair of Mathematical Finance at the University of York. He has authored about 50 research publications and four books. He has supervised four PhD dissertations and around 80 MSc dissertations in mathematical finance.
Table of Contents
Preface; 1. Probability space; 2. Probability distributions and random variables; 3. Product measure and independence; 4. Conditional expectation; 5. Sequences of random variables; Index.