This paper proposes a discrete-time risk model that has a certain type of correlation between premiums and claim amounts. It is motivated by the well-known bonus-malus system (also known as the no claims discount) in the car insurance industry. Such a system penalises policyholders at fault in accidents by surcharges, and rewards claim-free years by discounts. For simplicity, only up to three levels of premium are considered in this paper and recursive formulae are derived to calculate the ultimate ruin probabilities.Explicit expressions of ruin probabilities are obtained in a simplified case. The impact of the proposed correlation between premiums and claims on ruin probabilities is examined through numerical examples. In the end, the joint probability of ruin and deficit at ruin is also considered.
Wu, X., Chen, M., Guo, J., & Jin, C. (2015). On a discrete-time risk model with claim correlated premiums. Annals of Actuarial Science, 9(2), 322-342. [1748-4995]. https://doi.org/10.1017/S1748499515000032