Section: Overall Objectives

Overall Objectives

The Inria project team MathRisk team was created in 2013. It is the follow-up of the MathFi project team founded in 2000. MathFi was focused on financial mathematics, in particular on computational methods for pricing and hedging increasingly complex financial products. The 2007 global financial crisis and its “aftermath crisis” has abruptly highlighted the critical importance of a better understanding and management of risk. The project MathRisk has been reoriented towards mathematical handling of risk, and addresses broad research topics embracing risk measurement and risk management, modeling and optimization in quantitative finance, but also in other related domains where risk control is paramount. The project team MathRisk aims both at producing mathematical tools and models in these domains, and developing collaborations with various institutions involved in risk control. Quantitative finance remains for the project an important source of mathematical problems and applications. Indeed, the pressure of new legislation leads to a massive reorientation of research priorities, and the interest of analysts shifted to risk control preoccupation.

The scientific issues related to quantitative finance we consider include systemic risk and contagion modeling, robust finance, market frictions, counterparty and liquidity risk, assets dependence modeling, market micro-structure modeling and price impact. In this context, models must take into account the multidimensional feature and various market imperfections. They are much more demanding mathematically and numerically, and require the development of risk measures taking into account incompleteness issues, model uncertainties, interplay between information and performance and various defaults.

Besides, financial institutions, submitted to more stringent regulatory legislations such as FRTB or XVA computation, are facing practical implementation challenges which still need to be solved. Research focused on numerical efficiency remains strongly needed in this context, renewing the interest for the numerical platform Premia (http://www.premia.fr) that Mathrisk is developing in collaboration with a consortium of financial institutions.

While these themes arise naturally in the world of quantitative finance, a number of these issues and mathematical tools are also relevant to the treatment of risk in other areas as economy, social insurance and sustainable development, of fundamental importance in today's society. In these contexts, the management of risk appears at different time scales, from high frequency data to long term life insurance management, raising challenging renewed modeling and numerical issues.

The MathRisk project is strongly involved in the development of new mathematical methods and numerical algorithms. Mathematical tools include stochastic modeling, stochastic analysis, in particular stochastic (partial) differential equations and various aspects of stochastic control and optimal stopping of these equations, nonlinear expectations, Malliavin calculus, stochastic optimization, dynamic game theory, random graphs, martingale optimal transport (especially in relation to numerical considerations), long time behavior of Markov processes (with applications to Monte-Carlo methods) and generally advanced numerical methods for effective solutions.