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To the best of the authors’ knowledge, this book is the first reference to include both mathematical teaching with multiple exercises that have detailed solutions, focusing on discrete martingales and their application to financial markets, and practical work with solutions, using the software R. Special attention is paid to the Cox, Ross and Rubinstein model in discrete time.

This book is meant for students at the master’s or doctoral level who are specializing in applied mathematics or finance as well as teachers, researchers in the field of economics or actuarial science, professionals working in the various finance sectors, or any other person who may be interested in a rigorous and accessible mathematical construction of the tools and concepts used in financial mathematics or the application of the martingale theory in finance. Finally, the practical work on optimal portfolio management in ssss1, as well as the study of American options in ssss1, may serve as an elementary introduction to stochastic control problems.