Nonlinear methods for financial risk management

Scientific project

This three-year joint research project aims to develop advanced risk management techniques for derivatives. In this way, we hope to solve some of the current problems facing the main players in the financial markets and in particular insurance companies. Indeed, the latter have developed and marketed structured products of very long maturity and notional importance (for example Variable Annuities). In practice, the usual short-term risk management techniques for small-scale products are no longer applicable. With these new products, companies are exposed to significant market risks (stocks, interest rates and volatility, for example), market imperfections and changes in market parameters. From a theoretical standpoint, the classical approach based on stochastic but linear mathematical models is also out-dated for this type of product. We therefore need to develop new models that will be strongly non-linear. Doing so will require new methods of numerical resolution, which can be used in practice.

To meet these challenges, our project focuses mainly on two points; on the one hand, the development of models that realistically address the main market imperfections, recalibration problems, impact phenomena and regulatory constraints Imposed by regulators; and on the other, the implementation of effective numerical methods to resolve the issue of valuation and coverage in these new models. This project will benefit fully from the exchange of expertise between the AXA team and the academic team in the course of its three years duration. The project will also result in scientific publications in top-ranked international journals. Finally, it will organize two conferences on the topic of financial risk management to raise the awareness of professional and academic actors about new developments in this field.