On a discrete-time risk model with claim correlated premiums

Xueyuan Wu; Min Chen; Junyi Guo; Can Jin

doi:10.1017/S1748499515000032

On a discrete-time risk model with claim correlated premiums

Xueyuan Wu, Min Chen, Junyi Guo, Can Jin

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Article number	1748-4995
Pages (from-to)	322-342
Number of pages	21
Journal	Annals of Actuarial Science
Volume	9
Issue number	2
DOIs	https://doi.org/10.1017/S1748499515000032
Publication status	Published - 21 Jul 2015
Externally published	Yes

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10.1017/S1748499515000032

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title = "On a discrete-time risk model with claim correlated premiums",

abstract = "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.",

author = "Xueyuan Wu and Min Chen and Junyi Guo and Can Jin",

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AU - Jin, Can

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N2 - 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.

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On a discrete-time risk model with claim correlated premiums

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