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

TL;DR

This paper introduces a flexible mixed regression model with random effects for more accurate risk classification and ratemaking in automobile insurance, improving data fit and premium accuracy.

Contribution

It develops the Mixed LRMoE model with a scalable variational algorithm for better risk inference and applies it successfully to real insurance data.

Findings

The model provides a better fit to insurance claim data.

Posterior premiums reflect claim history more accurately.

The approach is scalable to large portfolios.

Abstract

A well-designed framework for risk classification and ratemaking in automobile insurance is key to insurers' profitability and risk management, while also ensuring that policyholders are charged a fair premium according to their risk profile. In this paper, we propose to adapt a flexible regression model, called the Mixed LRMoE, to the problem of a posteriori risk classification and ratemaking, where policyholder-level random effects are incorporated to better infer their risk profile reflected by the claim history. We also develop a stochastic variational Expectation-Conditional-Maximization algorithm for estimating model parameters and inferring the posterior distribution of random effects, which is numerically efficient and scalable to large insurance portfolios. We then apply the Mixed LRMoE model to a real, multiyear automobile insurance dataset, where the proposed framework is shown to offer better fit to data and produce posterior premium which accurately reflects policyholders' claim history.