CAS Exam 7 Spring 2016, Question 11
Study guide: Exam 7
An actuary is building a stochastic chain ladder model and is considering the following distributions:
- Over-Dispersed Poisson
- Over-Dispersed Negative Binomial
- Normal
Given the following information:
- Actual accident year 2015 losses at 12 months: $50,000
- Estimated chain-ladder accident year 2015 losses at 24 months: $75,000
Part a (1.5 points)
For each of the following distributions, calculate the variance of the accident year 2015 losses at 24 months.
- i. Over-dispersed Poisson model with
\varphi = 1.5. - ii. Over-dispersed negative binomial model with
\varphi = 1.25. - iii. Normally distributed model with
\varphi = 1.75.
Part b (0.5 points)
The actuary wants to use a model where the connection to the chain ladder method is immediately apparent. Identify and briefly explain which of the three models under consideration would achieve this.
Part c (0.5 points)
The loss development triangle being used has a column of incremental values with a negative sum. The actuary wants to use a model that does not require adjustments to the data. Identify and briefly explain which of the three models under consideration would achieve this.
Answer this question and see the worked solution
Concepts tested
- Bayesian
- Chain Ladder Method
- Dispersion Parameter
- Over-Dispersed Poisson Model
- Over-Dispersed Negative Binomial Model
- Stochastic Reserving