Pricing foreseeable and unforeseeable risks in insurance portfolios

Weihong Ni , Corina Constantinescu , Alfredo D Egídio dos Reis , Véronique Maume-Deschamps (1, 2)

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique

In this manuscript we propose a method for pricing insurance products that cover not only traditional risks, but also unforeseen ones. By considering the Poisson process parameter to be a mixed random variable, we capture the heterogeneity of foreseeable and unforeseeable risks. To illustrate, we estimate the weights for the two risk streams for a real dataset from a Portuguese insurer. To calculate the premium, we set the frequency and severity as distributions that belong to the linear exponential family. Under a Bayesian setup , we show that when working with a finite mixture of conjugate priors, the premium can be estimated by a mixture of posterior means, with updated parameters, depending on claim histories. We emphasise the riskiness of the unforeseeable trend, by choosing heavy-tailed distributions. After estimating distribution parameters involved using the Expectation-Maximization algorithm, we found that Bayesian premiums derived are more reactive to claim trends than traditional ones.

Mots clés: Mixed Poisson processes; Foreseeable risks; Unforeseeable risks; Bayesian estima- tion; Ratemaking; Experience rating; Bonus-malus; EM algorithm

Domaines: Probabilités [math.PR]

Weihong Ni, Corina Constantinescu, Alfredo D Egídio dos Reis, Véronique Maume-Deschamps. Pricing foreseeable and unforeseeable risks in insurance portfolios. 2020. ⟨hal-02899053⟩