Payments Per Claim Model of Outstanding Claims Reserve Based on Fuzzy Linear Regression

  • Chun Yan
  • Qian Liu
  • Jiahui Liu
  • Wei LiuEmail author
  • Meixuan Li
  • Man Qi


There are uncertainties in factors such as inflation. Historical data and variable values are ambiguous. They lead to ambiguity in the assessment of outstanding claims reserves. The payments per claim model can only perform point estimation. But the fuzzy linear regression is based on fuzzy theory and can directly deal with uncertainty in data. Therefore, this paper proposes a payments per claim model based on fuzzy linear regression. The linear regression method and fuzzy least square method are used to estimate the parameters of the fuzzy regression equation. And the estimated results are introduced into the payments per claim model. Then, the predicted value of each accident reserve is obtained. This result is compared with that of the traditional payments per claim model. And we find that the payments per claim model of estimating the fuzzy linear regression parameters based on the linear programming method is more effective. The model gives the width of the compensation amount for each accident year. In addition, this model solves the problem that the traditional payments per claim model cannot measure the dynamic changes in reserves.


Outstanding claims reserve Payments per claim model Fuzzy linear regression Linear programming Least square method 



This work was financially supported by the Project of National Natural Science Foundation of China(61502280,61472228).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  2. 2.College of Computer Science and EngineeringShandong University of Science and TechnologyQingdaoChina
  3. 3.Department of ComputingCanterbury Christ Church UniversityCanterburyUK

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