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Analysis of Relativity Premium in Bonus-Malus System Based on Optimal Linear Method

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  • Yu Chen
  • Long Li

Abstract

A bonus-malus system plays a very important role in actuarial mathematics through determining its relativity premium, which is extensively used in automobile insurance. There are many ways including Bayesian estimator and ordinary linear estimator to calculate the relativity premium. There is no doubt that Bayesian estimator is the most accurate estimator; however, it is undesirable for commercial purposes for its rather irregular pattern. This paper aims to introduce an optimal linear estimator for relativity premium, which has a simple pattern and is obtained under the quadratic loss function such that the result is close to Bayesian method. The Loimaranta efficiency of such an optimal linear estimator has been studied and compared with the two methods mentioned above.

Suggested Citation

  • Yu Chen & Long Li, 2014. "Analysis of Relativity Premium in Bonus-Malus System Based on Optimal Linear Method," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, September.
    • Handle: RePEc:hin:jnlmpe:846407
    DOI: 10.1155/2014/846407
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