A Credibility Index Approach for Effective a Posteriori Ratemaking with Large Insurance Portfolios

Credibility, experience rating and more recently the so-called a posteriori ratemaking in insurance consists in the determination of premiums that account for both the policyholders' attributes and their claim history. The models designed for such purposes are known as credibility models and fall under the same framework of Bayesian inference in statistics. Most of the data-driven models used for this task are mathematically intractable due to their complex structure, and therefore credibility premiums must be obtained via numerical methods e.g simulation via Markov Chain Monte Carlo. However, such methods are computationally expensive and even prohibitive for large portfolios when these must be applied at the policyholder level. In addition, these computations are "black-box" procedures for actuaries as there is no clear expression showing how the claim history of policyholders is used to upgrade their premiums. In this paper, we address these challenges and propose a methodology to derive a closed-form expression to compute credibility premiums for any given Bayesian model. We do so by introducing a credibility index, that works as an efficient summary statistic of the claim history of a policyholder, and illustrate how it can be used as the main input to approximate any credibility formula. The closed-form solution can be used to reduce the computational burden of a posteriori ratemaking for large portfolios via the same idea of surrogate modeling, and also provides a transparent way of computing premiums from which practical interpretations and risk assessments can be performed.

READ FULL TEXT

page 24

page 25

research
06/17/2021

Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench

Inferring parameter distributions of complex industrial systems from noi...
research
04/15/2021

Robust Generalised Bayesian Inference for Intractable Likelihoods

Generalised Bayesian inference updates prior beliefs using a loss functi...
research
02/03/2020

Predictive Risk Analysis in Collective Risk Model: Choices between Historical Frequency and Aggregate Severity

Typical risk classification procedure in insurance is consists of a prio...
research
11/21/2018

Surrogate-assisted parallel tempering for Bayesian neural learning

Parallel tempering addresses some of the drawbacks of canonical Markov C...
research
02/22/2020

Bayesian Computing in the Statistics and Data Science Curriculum

Bayesian statistics has gained great momentum since the computational de...
research
09/30/2022

A Posteriori Risk Classification and Ratemaking with Random Effects in the Mixture-of-Experts Model

A well-designed framework for risk classification and ratemaking in auto...
research
08/07/2021

Bayesian L_1/2 regression

It is well known that bridge regression enjoys superior theoretical prop...

Please sign up or login with your details

Forgot password? Click here to reset