Approximate Bayesian Computations to fit and compare insurance loss models

Pierre-Olivier Goffard (1, 2, 3) , Patrick Laub (1, 2, 1)

1 UCBL - Université Claude Bernard Lyon 1
2 ISFA - Institut de Science Financière et d'Assurances
3 LSAF - Laboratoire de Sciences Actuarielles et Financières [Lyon]

Approximate Bayesian Computation (ABC) is a statistical learning technique to calibrate and select models by comparing observed data to simulated data. This technique bypasses the use of the likelihood and requires only the ability to generate synthetic data from the models of interest. We apply ABC to fit and compare insurance loss models using aggregated data. We present along the way how to use ABC for the more common claim counts and claim sizes data. A state-of-the-art ABC implementation in Python is proposed. It uses sequential Monte Carlo to sample from the posterior distribution and the Wasserstein distance to compare the observed and synthetic data. MSC 2010 : 60G55, 60G40, 12E10.

Mots clés: Bayesian statistics; approximate Bayesian computation; likelihood- free inference; risk management

Domaines: Statistiques [stat]; Applications [stat.AP]; Gestion des risques [q-fin.RM]; Calcul [stat.CO]; Méthodologie [stat.ME]

Pierre-Olivier Goffard, Patrick Laub. Approximate Bayesian Computations to fit and compare insurance loss models. 2020. ⟨hal-02891046v1⟩