Paid-incurred chain reserving method with dependence modeling. (English) Zbl 1281.91099
Summary: The paid-incurred chain (PIC) reserving method is a claims reserving method that allows to combine claims payments and incurred losses information in a mathematical consistent way. The main criticism on the original Bayesian log-normal PIC model presented in [M. Merz and M. V. Wüthrich, Insur. Math. Econ. 46, No. 3, 568–579 (2010; Zbl 1231.91217)] is that it does not respect dependence properties within the observed data. In the present paper, we extend the original Bayesian log-normal PIC model so that dependence is modeled in an appropriate way.
MSC:
| 91B30 | Risk theory, insurance (MSC2010) |
| 60K10 | Applications of renewal theory (reliability, demand theory, etc.) |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
Keywords:
claims reserving; outstanding loss liabilities; ultimate loss prediction; claims payments; claims incurred; incurred losses; prediction uncertainty; paid-incurred chain model; PIC reserving methodCitations:
Zbl 1231.91217References:
| [1] | DOI: 10.1016/0167-6687(93)90240-P · Zbl 0800.62678 · doi:10.1016/0167-6687(93)90240-P |
| [2] | A Course in Credibility Theory and its Applications (2005) · Zbl 1108.91001 |
| [3] | Convex Optimization (2004) · Zbl 1058.90049 |
| [4] | DOI: 10.2143/AST.15.2.2015027 · doi:10.2143/AST.15.2.2015027 |
| [5] | DOI: 10.1007/BF02808969 · doi:10.1007/BF02808969 |
| [6] | CAS E-Forum Fall 2008 pp 272– (2008) |
| [7] | DOI: 10.1016/j.insmatheco.2010.02.004 · Zbl 1231.91217 · doi:10.1016/j.insmatheco.2010.02.004 |
| [8] | Stochastic Claims Reserving Methods in Insurance (2008) · Zbl 1273.91011 |
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