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Paid-incurred chain claims reserving method. (English) Zbl 1231.91217
Summary: We present a novel stochastic model for claims reserving that allows us to combine claims payments and incurred losses information. The main idea is to combine two claims reserving models (J. Hertig’s model [ASTIN Bull. 15, No. 2, 171–183 (1985)] and D. Gogol’s model [Insur. Math. Econ. 12, No. 3, 297–299 (1993; Zbl 0800.62678)]) leading to a log-normal paid-incurred chain (PIC) model. Using a Bayesian point of view for the parameter modelling we derive in this Bayesian PIC model the full predictive distribution of the outstanding loss liabilities. On the one hand, this allows for an analytical calculation of the claims reserves and the corresponding conditional mean square error of prediction. On the other hand, simulation algorithms provide any other statistics and risk measure on these claims reserves.

MSC:
91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62F15 Bayesian inference
62P05 Applications of statistics to actuarial sciences and financial mathematics
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