CAS Exam 7 Spring 2016, Question 15
Study guide: Exam 7
An actuary is retrospectively testing the general applicability of the Mack stochastic reserving model for Products Liability using incurred loss triangles from 20 insurance companies.
The following procedure was performed:
- The Mack model was used to fit each insurer's incurred loss triangle as of 10 years before the latest available annual data.
- A lognormal distribution was derived for each triangle by matching the mean and standard deviation from the Mack model results.
- Percentiles for each insurer's actual 10-year loss emergence were calculated assuming the lognormal distributions described above.
Given the following percentiles for each company's actual loss development within the distribution derived with the Mack model, in ascending order:
12, 29, 37, 40, 44, 45, 49, 50, 51, 52, 53, 58, 61, 62, 66, 67, 69, 71, 72, 84
Part a (1 point)
Determine whether the model is validated by applying the Kolmogorov-Smirnov test at the 5% confidence level, where the critical value is 30.4.
Part b (0.5 points)
Identify two reasons why loss reserve models often do not accurately predict the distribution of outcomes.
Part c (0.75 points)
Identify one shortcoming of the Mack model. Propose an alternative model and briefly explain a feature of the alternative model that addresses this shortcoming,
Answer this question and see the worked solution
Concepts tested
- Bayesian
- Chain Ladder Method
- Hypothesis Testing
- PP Plot
- Leveled Chain Ladder Model
- Correlated Chain Ladder Model
- Mack Chain Ladder Model
- Unpaid Claim Distribution
- Stochastic Reserving