All talks are 30 minutes long and should be as accessible as possible.

The idea is to have sufficient time for the speakers to properly motivate their work and introduce the questions and state of the answers in their research area, while not having enough time to delve too deep into technical considerations that would only benefit other specialists of the area. The theme of the conference are probability, numerics and finance. Numerics essentially refers to probabilistic numerical methods, or methods for probabilistic problems.

## ICERM - Robust Methods in Probability & Finance

Finance here is meant to encompass, on the one hand, the questions of management pricing and hedging of derivatives and the problems of optimal portfolio choice, which are classically associated with the phrase mathematical finance, but also, on the other hand, questions of interest for hedge funds and economists market microstructure, limit order books, systemic risk, ….

Presentation This conference for active young researchers PhD students, postdocs, early career professors aims at gathering about 30 participants in conditions that facilitate the interactions. Mathematical probability has a wider range of applications than any other area of applied mathematics. Game theory has become ubiquitous.

### Robust Methods in Probability & Finance

It is fundamental to theoretical economics and increasingly important in the other social sciences, in computer science, and even in pure mathematics. It is a remarkably broad mathematical framework, because games can have any number of players and any number of different rules for how they play, what information they have, and what and how they win. Our book uses only games of a very special kind—perfect-information games.

We show that the notion of probability emerges from certain simple perfect-information games. If there is one piece of information or advice that you would want your audience to take away from your book, what would that be?

- Mathematical finance - Wikipedia.
- Markov Processes. An Introduction for Physical Scientists;
- New Testament Textual Criticism: The Application of Thoroughgoing Principles: Essays on Manuscripts and Textual Variation (Supplements to Novum Testamentum).
- Mind Over Mood: Change How You Feel by Changing the Way You Think.

Everyone knows that the theory of mathematical probability began with calculations in games of chance. But that was long ago. Bringing back the language of betting can help everyone understand what is really going on.

## Mathematics, Probability and Statistics for Finance

The book has something to say to everyone who develops and uses mathematical probability: pure mathematicians who are proving new theorems in probability, applied mathematicians who are using probability in statistics, machine learning, engineering, or business, and philosophers who are exploring the meaning of probability across the sciences. The book is ideal for study at the graduate level. Each chapter has theorems and proofs, but most chapters also include a great deal of supplementary explanation. The book relates our theory to the established theory with a depth that was not possible in This explanation of the relationship between the two theories makes the new book essential to a full understanding of the established theory.

World-wide interest in game-theoretic probability itself has grown substantially since we published Probability and Finance in Workshops on the theory have been held and Britain, North America, and Japan. Many of the new results we report are due to a research group in Japan that was initiated by Kei Takeuchi and subsequently led by Akimichi Takemura.

The largest group of mathematicians now working on game-theoretic probability is in the area of mathematical finance. The fourth part of our book, which is devoted to this topic, is the result of interaction between Vovk, the Japanese school, and European students of probability-free finance. I expect that this part of the book will be foundational for further work in probability-free finance. The abstract theory in the second half of the book shows that game-theoretic probability is also closely related to imprecise probability, a field of research that has become increasingly active across the world during the past twenty years.

### Measure Theory

Much of the research now published under the rubric of imprecise probabilities could equally well be called research in game-theoretic probability. I believe that our book will be essential reading for students of imprecise probability. The game-theoretic picture of probability is also poised to become important in mathematical statistics and philosophy. In statistics, testing-by-betting is poised to address the current acute dissatisfaction with p-values.

In addition to being a report on your research, your book is also a teaching resource. Exercises for the student are given at the end of each chapter. What led you to include exercises?

## Book Review - Probability and Finance: It's Only a Game!

We have so much new to say that we needed to leave some of the details for the reader to work out. I packaged some of these details as exercises in order to provide the reader with some guidance. We then found it natural to add simpler exercises to help readers with less background get started.

The result will enable researchers interested in game-theoretic probability and its applications to include it in their teaching, whether or not they use other books as primary textbooks. What is it about the area of game-theoretic probability and finance that fascinates you? What does probability mean? Is it objective or subjective?