Bonus-malus Systems vs Delays in Claims Reporting and Settlement: Analysis of Ruin Probabilities

TL;DR

This paper analyzes how delays in claims reporting and settlement, along with claim correlations, affect ruin probabilities in a risk model with time-varying premiums, providing insights into optimal premium principles.

Contribution

It introduces a discrete-time risk model incorporating claim delays and correlations, and compares premium principles based on reported versus settled claims.

Findings

Higher by-claim delays decrease ruin probabilities under certain conditions.

Stronger correlation between claims increases ruin probabilities.

Premiums based on settled claims lead to higher ruin probabilities, especially with high delay likelihood.

Abstract

Our paper explores a discrete-time risk model with time-varying premiums, investigating two types of correlated claims: main claims and by-claims. Settlement of the by-claims can be delayed for one time period, representing real-world insurance practices. We examine two premium principles based on reported and settled claims, using recursively computable finite-time ruin probabilities to evaluate the performance of time-varying premiums. Our findings suggest that, under specific assumptions, a higher probability of by-claim settlement delays leads to lower ruin probabilities. Moreover, a stronger correlation between main claims and their associated by-claims results in higher ruin probabilities. Lastly, the premium adjustment principles based on settled claims experience contribute to higher ruin probabilities compared to those based on reported claims experience, assuming all other factors remain constant. Notably, this difference becomes more pronounced when there is a high likelihood of by-claim delays.