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This book provides an introduction to probabilistic methods in finance, based on stochastic models in discrete time. It is aimed primarily at graduate students in mathematics but may also benefit mathematicians in academia and the financial industry.

In this fifth edition, the entire text has been thoroughly revised to enhance clarity and completeness. This includes new sections on

Hans Föllmer is Professor emeritus at the Humboldt University of Berlin. He has also serves as Andrew D. White Professor-at-Large at Cornell University and Rothschild Distinguished Visiting Fellow, Isaac Newton Institute, Cambridge. He is widely known for his contributions to probability theory, stochastic analysis and mathematical finance. He was the recepient of the prestigious Cantor medal in 2006

Alexander Schied is a Professor and University Research Chair in the Department of Statistics and Actuarial Science at the University of Waterloo. His research is in probability theory and stochastic analysis with applications to mathematical finance and economics. He is currently Co-Editor of the journal Finance and Stochastics and member of several other editorial boards, including Applied Mathematics and Optimization, Mathematical Finance, the SIAM Journal on Financial Mathematics, and the SIAM Book Series on Financial Mathematics.