Quantile credibility models with common effects

Abstract

Different from classical Bühlmann and Bühlmann Straub credibility models in which independence between different risks are assumed, this paper takes dependence between risks into consideration and extends the classical Bühlmann model by introducing a common stochastic shock element. What is more, instead of relying on complete information of historical data, we aim to derive the premium using quantile of the available data. By the method of linear regression, we manage to obtain the quantile credibility premium with common effects. Our result is the generalization of existing results in credibility theory. Both quantile credibility model proposed by Pitselis (2013) and credibility premium for models with dependence induced by common effects obtained by Wen et al. (2009) are special cases of our model. Numerical simulations are also presented to illustrate the impact of quantile credibility with common effect.