Actuarial Notes

CAS Exam 7 Spring 2017, Question 11

Study guide: Exam 7

Given the following information:

  • Cumulative reported losses at 24 months for accident year 2015 are $9,000
  • The following reported development factors were derived:
Age Loss Development Factor Cumulative Development Factor % Reported
12 2.000 3.000 33.3%
24 1.364 1.500 66.7%
36 1.073 1.100 90.9%
48 1.025 1.025 97.6%
60 1.000 1.000 100.0%
  • Incremental losses, C_{ij}, follow an over-dispersed Poisson distribution with mean x_i y_i and variance \varphi x_i y_i
  • The variable x_i represents the expected ultimate losses for accident year i.
  • The variable y_j represents the proportion of ultimate losses that emerge in development year j.
  • The prior distribution for x_i is gamma with mean \alpha_i / \beta_i and variance \alpha_i / \beta_i^2
  • The dispersion parameter, \varphi, for the over-dispersed Poisson distribution is 9.125
  • The accident year 2015 estimates for \alpha and \beta are 100 and 0.01234 respectively.
  • The mean of C_{ij} for this Bayesian model is:

Z_{ij}(\lambda_j - 1)D_{i,j-1} + (1 - Z_{ij})(\lambda_j - 1)M_i \frac{1}{\lambda_j \lambda_{j+1} \cdots \lambda_n}, \quad \text{where } Z_{ij} = \frac{\sum_{k=1}^{j-1} y_k}{\beta_i \varphi + \sum_{k=1}^{j-1} y_k}

  • \lambda_j is the incremental chain ladder loss development factor for development year j.
  • D_{ij} is the cumulative losses for accident year i as of development year j.

Part a (2 points)

Calculate the incremental losses for accident year 2015 expected to emerge between 24 and 48 months of development using the model.

Part b (0.5 points)

Identify and briefly describe what parameter in the model would have to change in order to produce IBNR estimates closer to chain ladder indications.

Answer this question and see the worked solution

Concepts tested

More questions from this set