Résumé: In traditional quantile credibility models, it is typically assumed that claims are independent across different risks. Nevertheless, there are numerous scenarios where dependencies among insured individuals can emerge, thereby breaching the independence assumption. This study focuses on examining the quantile credibility model and extending some established results within the context of an equal correlation structure among risks. Specifically, we compute the credibility premiums for both homogeneous and inhomogeneous cases utilizing the orthogonal projection method

Résumé: This paper generalizes the quadratic framework introduced by Le Courtois (2016) and Sumpf (2018), to obtain new credibility premiums in the balanced case, i.e. under the balanced squared error loss function. More precisely, the authors construct a quadratic credibility framework under the net quadratic loss function where premiums are estimated based on the values of past observations and of past squared observations under the parametric and the non-parametric approaches, this framework is useful for the practitioner who wants to explicitly take into account higher order (cross) moments of past data.

Résumé: In this paper, we focus on estimation of credibility premium in the case if we know nothing about the probability distribution of claims Xi(i = 12 n) except observation data. To treat this case, we apply the Maximum Entropy Method (MEM henceforth) under the balanced loss function to obtain a new credibility premium. Furthermore, a numerical simulation and an application to real data are presented to compare the credibility premium obtained in the present paper with that of Gomez-Deniz (2006) by using mean square Errors as an evaluation criterion.

Résumé: In this paper, we consider the Zeghdoudi distribution as the conditional distribution of Xn | θ, we focus on estimation of the Bayesian premium under three loss functions (squared error which is symmetric, Linex and entropy, which are asymmetric), using non-informative and informative priors (the extension of Jeffreys and Gamma priors) respectively. Because of its difficulty and non linearity, we use a numerical approximation for computing the Bayesian premium.

Résumé: We consider the Gamma Lindley distribution (GaL) as the conditional distribution of (X⃓θ,γ) , we focus on the estimation of the Bayesian premium under squared error loss function (symmetric) and Linex loss function (asymmetric), using informative priors (the Gamma prior). Because of its difficulty and non-linearity, we use a numerical approximation for computing the Bayesian premium. Finally, a simulation and comparative study with varying sample sizes are given.