# Estimation of foreseeable and unforeseeable risks in motor insurance

## TL;DR

This paper develops a Bayesian-based model to estimate and price both foreseeable and unforeseeable risks in motor insurance, addressing challenges in separating and quantifying latent high-uncertainty risks.

## Contribution

It introduces a novel model that separates claim counts and severities for different risk streams, with a new premium calculation and parameter estimation method using EM algorithm.

## Key findings

- Effective separation of claim types demonstrated
- Accurate estimation of high-uncertainty risks achieved
- Enhanced premium adjustment strategies proposed

## Abstract

This project works with the risk model developed by Li et al. (2015) and quests modelling, estimating and pricing insurance for risks brought in by innovative technologies, or other emerging or latent risks. The model considers two different risk streams that arise together, however not clearly separated or observed. Specifically, we consider a risk surplus process where premia are adjusted according to past claim frequencies, like in a Bonus-Malus (BM) system, when we consider a classical or historical risk stream and an unforeseeable risk one. These are unknown risks which can be of high uncertainty that, when pricing insurance (ratemaking and experience rating), suggest a sensitive premium adjustment strategy. It is not clear for the actuary to observe which claim comes from one or the other stream. When modelling such risks it is crucial to estimate the behaviour of such claims, occurrence and their severity. Premium calculation must fairly reflect the nature of these two kinds of risk streams. We start proposing a model, separating claim counts and severities, then propose a premium calculation method, and finally a parameter estimation procedure. In the modelling we assume a Bayesian approach as used in credibility theory, a credibility approach for premium calculation and the use of the Expectation-Maximization (EM) algorithm in the estimation procedure.