The research programme “Impact of the Climate Transition in Insurance” focuses on the consequences of the climate transition on agricultural risk. In particular, we are developing fast and efficient estimation methods for massive data and numerical methods for risk measurements and dynamic preferences. SYNTHESIS OF RESEARCH WORK / YOUR RP SUM UP*The first theoretical developments concern efficient and fast estimation procedures for large datasets. These considerations are the subject of the ANR EFFI project led by A. Brouste at the Laboratoire Manceau de Mathématiques. For some generalized linear models (GLM) with categorical variables, explicit (maximum likelihood) estimators have been proposed. These estimators allow a fast and efficient calibration of GLMs which are used by insurers for the pricing of insurance products by substituting an explicit calculation to the numerical optimization method of gradient descent type. In addition, these new methods make it possible to study multiple effects, which is currently impossible to do in SAS or R. The Groupama teams are interested in this type of study on the claims databases of their agricultural crop insurance.
We are also developing, within this framework, estimators for simple effects only GLMs that do not fit into the previous framework. These alternative estimators are fast to compute but are not efficient (in the statistical sense). To obtain efficiency, Le Cam’s one-step estimation procedures are studied for different statistical experiments and are the subject of the development of a package for the free software R. We are currently planning to extend this procedure to GLMs. The extension is to be done for GLMs in the general case and for GLMs with categorical variables. The research programme with Groupama would be an opportunity to apply these new efficient and fast methods to agricultural risk data and to study the impact of the climate transition. The second theoretical development concerns systemic risk measures. These considerations are the subject of an ANR DREAMES project led by A. Matoussi (LMM-IRA). The computational aspects of (dynamic) risk measures for large multivariate systems are addressed as well as the sensitivity of risk allocations to various factors. Systemic risk measures (SRMs) allow to simultaneously assess the overall risk of the system, and to propose a risk transfer mechanism between heterogeneous actors that is optimal from the point of view of both the decision maker and the agents. This point of view is close to the classical framework of univariate monetary risk measures and the first objective is to extend this approach to a dynamic multivariate framework. In particular, the static framework developed in the paper does not allow to consider long-term problems, such as inter- and intra-generational risk transfers in pension systems, or heterogeneous life insurance portfolios. The second objective is to extend systemic risk measures to a dynamic framework to take into account complex dependencies between agents, or inflows and claim sizes in the case of life insurance portfolios. In the framework of this project, we intend to apply this whole SRM approach (theoretical, numerical and calibration) in actuarial and insurance problems affected by the climate transition.