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2 results

  • STOCHASTIC CLAIMS RESERVING VIA A BAYESIAN SPLINE MODEL WITH RANDOM LOSS RATIO EFFECTS

  • Guangyuan Gao, Shengwang Meng
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 48 / Issue 1 / January 2018
    Published online by Cambridge University Press:
    13 July 2017, pp. 55-88
    Print publication:
    January 2018

  • 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.

  • The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor

  • Thomas Mack
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 29 / Issue 2 / November 1999
    Published online by Cambridge University Press:
    29 August 2014, pp. 361-366
    Print publication:
    November 1999
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  • In Mack (1993), a formula for the standard error or chain ladder reserve estimates has been derived. In the present communication, a very intuitive and easily programmable recursive way of calculating the formula is given. Moreover, this recursive way shows how a tail factor can be implemented in the calculation of the standard error.