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Chinese Journal of Management Science ›› 2014, Vol. 22 ›› Issue (4): 9-16.

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Stochastic Reserves Development Methods Based on the Correlation Among Paid-Incurred Payments Data and Their Improvement

DUAN Bai-ge1, ZHANG Lian-zeng2   

  1. 1. School of Economics, Fudan University, Shanghai 200433, China;
    2. School of Economics, Nankai University, Tianjin 300071, China
  • Received:2011-08-09 Revised:2014-02-06 Online:2014-04-20 Published:2014-04-23

Abstract: Three stochastic reserves development methods are innovatively proposed in this paper considering the correlation between paid-incurred payments data, i.e. based on non-parametric Bootstrap method with pairwise resampling, based on bivariate normal distribution, and based on Copulas function. Combined the classic run-off triangles data in the non-life actuarial practice, a complete programming for three stochastic reserve development methods is provided based on the correlation with R software. Further, the complete predictive distributions of ultimate loss, outstanding claims reserves and IBNR are simulated. The proposed stochastic reserve development methods based on the correlation not only consider the correlation between the paid payments and the incurred payments, but also reflect the development difference of incurred and reported outstanding claims reserves in different accident years. Such ideas and methods considering correlation have important theoretical significance and practical value for multivariate reserving.

Key words: stochastic reserve development methods, multivariate reserving, Copulas function, Bootstrap method, bivariate normal distribution, predictive distribution

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