Objective Bayesian modelling of insurance risks with the skewed Student-t distribution

TL;DR

This paper develops an objective Bayesian method using a skewed Student-t distribution to model skewed insurance risk data, extending previous models by including an additional skewness parameter.

Contribution

It introduces a Bayesian approach with a new prior for degrees of freedom, specifically tailored for skewed Student-t distributions in insurance risk modeling.

Findings

Effective modeling of skewed insurance data

Application to Danish fire and US indemnity datasets

Demonstrates improved fit over symmetric models

Abstract

Insurance risks data typically exhibit skewed behaviour. In this paper, we propose a Bayesian approach to capture the main features of these datasets. This work extends the methodology introduced in Villa and Walker (2014a) by considering an extra parameter which captures the skewness of the data. In particular, a skewed Student-t distribution is considered. Two datasets are analysed: the Danish fire losses and the US indemnity loss. The analysis is carried with an objective Bayesian approach. For the discrete parameter representing the number of the degrees of freedom, we adopt a novel prior recently introduced in Villa and Walker (2014b).