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On a discrete-time risk model with claim correlated premiums

Published online by Cambridge University Press:  21 July 2015

Xueyuan Wu ,
Mi Chen ,
Junyi Guo  and
Can Jin
Xueyuan Wu*
Affiliation:
Department of Economics, The University of Melbourne, VIC 3010, Australia
Mi Chen
Affiliation:
School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
Junyi Guo
Affiliation:
School of Mathematical Sciences, Nankai University, Tianjin 300071, China
Can Jin
Affiliation:
Department of Economics, The University of Melbourne, VIC 3010, Australia
*
*Correspondence to: Xueyuan Wu, Department of Economics, The University of Melbourne, VIC 3010, Australia. Fax: +61 3 8344 6899. E-mail: xueyuanw@unimelb.edu.au
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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.

Keywords

Discrete-time risk modelNo claims discountBonus-malusRuin probabilityDeficit at ruinRecursion
Type
Papers
Information
Annals of Actuarial Science , Volume 9 , Issue 2 , September 2015 , pp. 322 - 342
Copyright
© Institute and Faculty of Actuaries 2015 

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