Location
Dates
Presentation
The CIMPA School Ordered Structures with Applications in Finance and Machine Learning is scheduled to take place from June 16-28, 2024 at the University of Carthage‘s IPEST campus.
The CIMPA School aims to foster multidisciplinary collaboration by promoting interactions between the various specialties offered. To achieve this, the school will focus on two key areas: mathematical finance and stochastic calculus, as well as machine learning. These two fields will be approached from the perspective of ordered structures, which are inherently multidisciplinary and have applications in logic, algebra, functional analysis, and computer science, as well as in finance, economics, and machine learning.
The school will offer courses on probability theory and stochastic computations in vector lattices and Banach lattices, as well as courses on machine learning and its applications in finance. Machine learning has become a crucial area of research in recent decades, and it has become increasingly important for the scientific community of vector lattices and Banach lattices to engage with it. In fact, recent research has suggested that ordered lattices could be a promising avenue for high-dimensional optimization in machine learning.
To emphasize the practical aspects of these topics, the afternoons of the school will be dedicated to tutorial and practical sessions, with morning sessions being plenary and taking place in the IPEST amphitheater. The afternoon sessions will be in small groups with a maximum of 20 participants to facilitate interactive learning and practical work.
Scientific program is available on the local website of the School: https://rgosa.net/cimpa-school-osafml/
Official language of the school: English
Administrative and scientific coordinators
Scientific program
Course 1: "introductory course - Il s'agit de présenter différentes situations où on est amené à introduire un (pré-) ordre en théorie des mathématiques financières. Ceci illustrera notamment le rôle important que joue la notion de cônes issus de la théorie des treillis et des (pré-) espaces de Riesz. On introduira aussi des notions telle que les ensembles aléatoires et leurs applications en finance.", Emmanuel LEPINETTE (Université Paris Dauphine, France)
Course 2: "introductory course - 1. Reminders on conditional expectation in L1-spaces. 2. Andô Douglas Theorem and characterization of the conditional expectation. 3. Basics of Riesz spaces, including bands, band projections, weak order units, order convergence, Freudenthal's theorem and functional calculus. 4. Conditional expectation operators on Dedekind complete Riesz spaces with a weak order unit, including various types of completions of Riesz spaces with a conditional expectation operator. 5. Multiplication in Riesz spaces. F-algebras and averaging operators. Lp type spaces. Ando-Douglas-Radon-Nikodym theorems in Riesz space. Modules over f-algebras and vector values norms. ", Wen-Chi KUO (University of the Witwatersrand, South Africa)
Course 3: "introductory course - This lecture series considers the core properties and key results in the theory of Markov processes and martingale theory. The course will begin with a recollection of the definitions of these types of processes in the probability setting as well as their generalization to vector lattice. Key concepts such as the Kolmogorov-Chapman theorem and time reversiblity will be discussed for Markov processes as well as hitting times. For martingale, the stopped processes will be discussed as well as the optional stopping theorems. Stochastic integrals and connections with abstract Bownian motion will also be looked at.", Bruce WATSON (University of the Witwatersrand, South Africa)
Course 5: "programming sessions - Il s’agit d’un cours pratique dans lequel les participants à l’école apprendront les techniques classiques de programmation en langage Python. Ils apprendront entre autres les bibliothèques mathématiques : Numpy et MatPlotLib. Il sera aussi question de se familiariser avec les bibliothèques de Machine Learning et notamment Scikit-learn et TensorFlow.", Meriem ELMANSOUR (Université Paris Dauphine-Tunis, Tunisia)
Course 7: "introductory course - L'énergie éolienne est tributaire de conditions météorologiques spécifiques. Une bonne prédiction améliorera la gestion d'un réseau d'éoliennes. Ce cours expliquera les récentes applications et découvertes en Machine Learning développées en collaboration avec l'opérateur de réseau électrique espagnol (REE) et leur application pratique dans le la gestion d'un réseau d'éoliennes. ", Ignacio VILLANUEVA (Universidad Complutense de Madrid, Spain)
Course 8: "advanced course - Sont présentés les principaux théorèmes de caractérisation d'équilibre d'un marché financier, sans coûts de transactions en un premier temps, à l'origine de la finance quantitative moderne. En un second temps, l’accent sera mis sur l’équilibre avec coûts de transaction et les techniques s’y attachant.", Yuri KABANOV (Université de Franche-Comté, France)
Course 9: "advanced course - We begin with an overview of measure preserving transformations and their Riesz space generalization (conditional expectation preserving systems). The first recurrence time will be introduced in the measure setting and in Riesz spaces along with the Poincare recurrence theorem and Kac's formula. With this foundation entropy of a system can be defined. Building on this an overview will be given of information theory and it Riesz space extension.", Jonathan HOMANN (North West University, South Africa)
Course 10: "introductory course - La détection de Fraude est un enjeu majeur dans le monde de la finance et des assurances. La fraude représente dans certains pays d’Afrique comme la Tunisie une part non négligeable des sinistres déclarés dans l’assurance automobile par exemple. Ce cours a pour but d’appliquer les notions vues tout au long de l’école dans une étude de cas concrète et sa résolution sur machine.", Enrique A. SÁNCHEZ-PÉREZ (Universidad Politécnica de Valencia, Spain)
Course 11: "exercise session - Travaux pratiques et dirigés lié au cours exposé par Yuri Kabanov.", Dorsaf CHÉRIF (Université de Carthage, Tunisia)
Course 12: "exercise session - Travaux pratiques et dirigés lié au cours exposé par Jonathan Homann.", Marwa MASMOUDI (Université de Carthage, Tunisia)
Course 13: "exercise session - Travaux pratiques et dirigés lié au cours exposé par Gael Collinet.", Ahlem KAABI (Holberton School, Tunisia)
Course 14: "exercise session - Travaux pratiques et dirigés lié au cours exposé par Pedro Tradacete.", Asma BEN RJEB (Université de Tunis EL MANAR, Tunisia)
Course 15: "exercise session - Travaux pratiques et dirigés lié au cours exposé par Bruce Watson.", Amal OMRANI (Université de Monastir, Tunisia)
Website of the school
How to participate
For registration and application to a CIMPA financial support, follow the instructions given here https://www.cimpa.info/en/node/40
Deadline for registration and application: March 15, 2024