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Stochastic claims reserving via a Bayesian spline model with random loss ratio effects. (English) Zbl 1390.62206

Summary: We propose a Bayesian spline model which uses a natural cubic \(B\)-spline basis with knots placed at every development period to estimate the unpaid claims. Analogous to the smoothing parameter in a smoothing spline, shrinkage priors are assumed for the coefficients of basis functions. The accident period effect is modeled as a random effect, which facilitate the prediction in a new accident period. For model inference, we use Stan to implement the no-U-turn sampler, an automatically tuned Hamiltonian Monte Carlo. The proposed model is applied to the workers’ compensation insurance data in the United States. The lower triangle data is used to validate the model.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
91B30 Risk theory, insurance (MSC2010)
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