CAS Exam 7 Spring 2012, Question 13
Study guide: Exam 9
Given the following data and estimates for a personal lines insurer:
| Current Business | Expected claim count | Expected claim severity |
|---|---|---|
| Auto | 6,800 | $700 |
| Homeowners | 9,000 | 750 |
| Loss Reserves | Claim count | Claim severity |
|---|---|---|
| Auto | 2,600 | $2,100 |
| Homeowners | 400 | 1,250 |
The insurer's total losses are modeled by a lognormal distribution with the following Value at Risk (VaR) amounts for certain percentiles:
\text{VaR}_{95} = 20{,}346{,}511\text{VaR}_{96} = 20{,}540{,}313\text{VaR}_{97} = 20{,}795{,}018\text{VaR}_{98} = 21{,}132{,}866\text{VaR}_{99} = 21{,}680{,}765
The risk based capital required for underwriting risk is given by the following factor based formula:
\text{TVaR}_{95} - \text{Expected Loss on Current Business} - \text{Loss Reserve}
Part a (1.5 points)
Calculate the estimated risk based capital required to support this insurer's underwriting risk.
Part b (1.5 points)
Briefly discuss three limitations with the above model, and suggest changes that would address each.
Part c (1 point)
The CEO of this insurer wants to reduce the risk based capital calculated in part a. above by half going forward. The CEO plans to achieve this goal by buying 50% quota share reinsurance on the entire book of business. Fully explain why that will not achieve this goal.
Answer this question and see the worked solution