This book is in the series
De Gruyter Textbook
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
stop-loss insurance contracts,
the Fatou property of law-invariant risk measures,
relative entropy,
Cover’s universal portfolios,
and numerous new exercises.
Hans Follmer is Professor emeritus at Humboldt University of Berlin. He was also Professor at ETH Zurich and the University of Bonn, Distinguished Visiting Professor at the National University of Singapore, and Andrew D. White Professor-at-Large at Cornell University.
Alexander Schied is Professor at the University of Waterloo and holds the Munich Re Chair in Stochastic Finance and a University Research Chair.
Mathematics
Probability and Statistics
Mathematics
Applied Mathematics
Business and Economics
Mathematics and Statistics for Economists
Mathematics
Business and Economics
Mathematics and Statistics for Economists
Statitistics
This book is in the series
Volume 40 | De Gruyter Series in Nonlinear Analysis and Applications
The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.
? Introduces dynamical systems for applications in biology and ecology
? Covers the main components in cross-diffusion systems and coexistence of geometry-affected steady states
? Discussed global existence and persistence of evolution processes
Mathematics
Analysis
Mathematics
Differential Equations and Dynamical Systems
Mathematics
Probability and Statistics
Mathematics
Applied Mathematics
This book is in the series
De Gruyter Textbook
Discrete Mathematics presents the material in an easily accessible manner. Beside the usual content (expanded a little bit), a special writing style is used.
We start with the natural numbers, function and relations, as well as the powerset lattice. The second chapter illustrates set theory with its laws and the Generalized Continuum Hypothesis. Chapter 3 delivers Boolean Algebra, with the double exponential formula for the # different boolean functions. The next chapter covers the induction, direct, and indirect proof. Chapter 5 presents combinatorics: Rules of sum, product, quotient, the pigeonhole principle, in/exclusion, permutation and binomial coefficient, plus Stirling numbers of 1st and 2nd kind as well as the Bell number; additionally, the recurrence relation with back- and forward reasoning is offered. We conclude with general and conditional probability, incl. the Monty Hall problem.
Discrete Mathematics presents the material in a lively fashion, including topics which are usually not presented. Providing an annex with questions and solutions it offers the chance to the readers worldwide to grasp the subject in this handy and clearly arranged treatise.
Excellent source for teaching the basics of discrete mathematics to computer scientists.
Includes exercises and worked out solutions.
Probability and statistics are subjects fundamental to data analysis, making them essential for efficient artificial intelligence. Although the foundational concepts of probability and statistics remain constant, what needs to be taught is constantly evolving.
The first half of the book introduces probability, conditional probability and the standard probability distributions in the traditional way. The second half considers the power of the modern computer and our reliance on technology to do the calculations for us.
Offering a fresh presentation that builds on the author's previous book, Understanding Statistics, this book includes exercises (with solutions at the rear of the book) and worked examples. Chapters close with a brief mention of the relevant R commands and summary of the content. Increasingly difficult mathematical sections are clearly indicated, and these can be omitted without affecting the understanding of the remaining material.
Aimed at first year graduates, this book is also suitable for readers familiar with mathematical notation.
Copyright 2026
ISBN 9781032454276
560 Pages 147 Color Illustrations
September 30, 2025 by Routledge
Multivariate Statistics and Machine Learning is a hands-on textbook providing an in-depth guide to multivariate statistics and select machine learning topics using R and Python software.
The book offers a theoretical orientation to the concepts required to introduce or review statistical and machine learning topics, and in addition to teaching the techniques, instructs readers on how to perform, implement, and interpret code and analyses in R and Python in multivariate, data science, and machine learning domains. For readers wishing for additional theory, numerous references throughout the textbook are provided where deeper and less “hands on” works can be pursued.
With its unique breadth of topics covering a wide range of modern quantitative techniques, user-friendliness and quality of expository writing, Multivariate Statistics and Machine Learning will serve as a key and unifying introductory textbook for students in the social, natural, statistical and computational sciences for years to come.