ANJA is joint research team between Inria, CNRS and Nantes University (Laboratoire Jean Leray). ANJA develops mathematical models based mainly on probabiliy theory and statistics in the field of social sciences, and in particular economy, finance, law and archeology.
A particular attention is paid to the so-called performative dimension of models: the performative effect is the fact that applying a mathematical model in social sciences has consequences very different from the ones that occur when application is in natural sciences. Indeed, models will typically tend to modify the reality they describe. For nstance, the enforcement of prudential regulations such as Solvency 2 – which are explitly required to be based on mathematical models – does transform insurance companies practices. Likewise, in the legal domain, the growing use of scales, for instance for children or spousla support, influences the behaviour of the various actors.
We develop theoretical methods in the fields of
- probability theory: as an example, we create stochastic models allowing us to describe in a precise way the irregularity of various phenomena observed in finance, and we build the associated stochastic calculus,
- statistics: among other things, we construct estimators permitting to identify our stichasitc models,
- machine learning: we develop learning methods that are fitted to the peculiarities of our applications in law.
As far as applications are concerned, we are specially interested in:
- measuring financial risks, as well as assessing the negative impact of prudential regulations,
- measuring legal risk, through the development of tools that allow one to assess it with approaches similar to the ones used for financial risk,