Journal of Mathematics and Modeling in Finance

Joint Partially Models for Dependent Frequency and Severity of Insurance Claims with using Spline Functions

Articles in Press

Document Type : Research Article

Author

Ehsan Bahrami Samani

Department of Statistics, Shahid Beheshti University, Tehran, Iran.

10.22054/jmmf.2026.92058.1274
Abstract
In this paper, the claim counts and claim amounts, both with and without missing values, are assumed to be correlated in the context of non-life insurance. The proposed methodology involves fitting joint random effects partially specified models based on the factorization of the joint distribution of claim counts and average claim amounts. Furthermore, the paper introduces joint partially aggregate claims models that account for correlated claim count and amount responses, addressing cases with missing values in both variables and incorporating nonignorable missing data mechanisms. To capture non-linear time effects on the joint model, various spline functions are employed. A full likelihood based estimation procedure is adopted to obtain maximum likelihood estimates for the parameters of the joint partial models involving correlated claim frequencies and severities. For data scenarios where both variables contain nonignorable missing values, a corresponding pure premium formula is derived. The performance of the proposed model is compared to that of the independent aggregate claims model through a simulation study, focusing on differences in the resulting pure premiums. To assess model sensitivity, influence analysis is conducted by examining how small perturbations in the average percent difference (APD) affect likelihood displacement using influence graphs. Finally, the methodology is applied to a real Iranian automobile insurance dataset.

Keywords

Partially aggregate claims model
Claim frequency
Claim severity
Missing Data
Spline functions
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Journal of Mathematics and Modeling in Finance

Articles in Press, Accepted Manuscript
Available Online from 05 July 2026

  • Receive Date 30 March 2026
  • Revise Date 28 June 2026
  • Accept Date 29 June 2026

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