Benoite de Saporta – författare

This book is entirely devoted to discrete time and provides a detailed introduction to the construction of the rigorous mathematical tools required for the evaluation of options in financial markets. Both theoretical and practical aspects are explored through multiple examples and exercises, for which complete solutions are provided. Particular attention is paid to the Cox, Ross and Rubinstein model in discrete time.The book offers a combination of mathematical teaching and numerous exercises for wide appeal. It is a useful reference 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, or professionals working in the various financial sectors.Martingales and Financial Mathematics in Discrete Time is also for anyone who may be interested in a rigorous and accessible mathematical construction of the tools and concepts used in financial mathematics, or in the application of the martingale theory in finance

Hidden Semi-Markov Models (HSMMs) have been extensively used for diverse applications where the objective is to analyze time series whose dynamics can be explained by a hidden process.A Comprehensive Guide to HSMM offers an accessible introduction to the framework of HSMM, covering the main methods and theoretical results for maximum likelihood estimation in HSMM. It also includes a unique review of existing R and Python software for HSMM estimation. The book then introduces less classical related topics, such as multi-chain HSMM and controlled HSMM, with an emphasis on the challenges related to computational complexity.This book is primarily intended for master's and PhD students, researchers and academic faculty in the fields of statistics, applied probability, graphical models, computer science and connected domains. It is also meant to be accessible to practitioners involved in modeling, analysis or control of time series in the fields of reliability, theoretical ecology, signal processing, finance, medicine and epidemiology.