This section of sample problems and solutions is a part of The Actuary’s Free Study Guide for Exam 6, authored by Mr. Stolyarov. This is Section 18 of the Study Guide. See an index of all sections by following the link in this paragraph.
Some of the questions here ask for short written answers. This is meant to give the student practice in answering questions of the format that will appear on Exam 6. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.
Some of the problems in this section were designed to be similar to problems from past versions of Exam 6, offered by the Casualty Actuarial Society. They use original exam questions as their inspiration – and the specific inspiration is cited to give students an opportunity to see the original. All of the original problems are publicly available, and students are encouraged to refer to them. But all of the values, names, conditions, and calculations in the problems here are the original work of Mr. Stolyarov.
Past Casualty Actuarial Society exams: 2007 Exam 6.
Original Problems and Solutions from The Actuary’s Free Study Guide
Problem S6-18-1. Similar to Question 36 from the 2007 CAS Exam 6. Explain why, for a retrospectively rated policy, retrospective premiums will increase at a decreasing rate as reported losses increase. Also explain why this would apply, in particular, to cases where catastrophic injuries make a person eligible for lifetime benefits.
Solution S6-18-1. The determination of retrospective premium is subject to per-occurrence caps on losses and also, typically, to a maximum premium amount. Thus, not the entire amount of every subsequent loss would be added retrospective premium, and the proportion of each subsequent loss’s contribution is probably going to decrease. With regard to cases where catastrophic injuries make a person eligible for lifetime benefits, the initial injury may not seem like one that will disable an individual for life. Later, as additional information is discovered, the loss would develop, and the cap and maximum premium would be quite likely to apply.
Problem S6-18-2. Similar to Question 34 from the 2007 CAS Exam 6.
(a) Why are medical malpractice paid loss data typically so sparse?
(b) What common aspects of medical malpractice settlements distort trends in loss severity for this type of insurance?
(a) Medical malpractice losses are paid out very slowly compared to losses for other coverages, and this results in sparse historical paid loss data for a particular experience period.
(b) Medical malpractice settlements are often paid out with extreme irregularity, and there is considerable variation in claims closed with no payment. Assuming a regular loss trend will therefore most often not reflect reality.
Problem S6-18-3. Similar to Question 37 from the 2007 CAS Exam 6. When the underlying loss exposure is evenly distributed throughout the policy period, why is estimating earned premium for an excess policy using the pro rata method still inappropriate?
Solution S6-18-3. An excess policy only pays when losses exceed a certain amount. If exposure is evenly distributed, it takes some time before losses are likely to exceed the attachment point of the excess policy. As losses approach the attachment point, the risk that the excess policy will pay out anything increases, and so more premium should be earned later in the policy term. Pro rata estimates of earned premium overstate the earned premium early on.
Problem S6-18-4. Similar to Question 39 from the 2007 CAS Exam 6. Define pure premium by reference to its constituent terms and name three events that are external to an insurance company but which could affect pure premium. For each event, specify the component of pure premium which would be affected.
Solution S6-18-4. Pure Premium = (Frequency)*(Severity).
The following is a sample response. Many other valid answers are possible.
1. An increased tendency for juries to award higher damages for particular types of cases might increase pure premium by raising claim severity.
2. An increased number of uninsured motorists on the road might increase the frequency of claims on uninsured motorists coverage.
3. A law that requires the insurer to cover a previously excluded exposure might increase the frequency of claims on the policies in question.
Problem S6-18-5. Similar to Question 28 from the 2007 CAS Exam 6. A primary insurer is a party to two reinsurance treaties: Treaty A is a 65% quota-share treaty. Treaty B is a $20 million in excess of $15 million catastrophe treaty. If a loss of $40 million occurs, would the primary insurer prefer (i) the situation where Treaty A inures to the benefit of Treaty B or (ii) the situation where Treaty B inures to the benefit of Treaty A? Explain your reasoning and show your calculations.
Solution S6-18-5. When a reinsurance treaty inures to the benefit of another, it is applied to the loss amount first, leaving the other reinsurance treaty to be benefited by the other reinsurer having to pay less.
Situation (i): Treaty A applies first and pays 65% of $40 million, or $26 million. The remaining loss amount is $14 million, which is not above the attachment point of the catastrophe treaty. So the catastrophe treaty pays nothing, and the primary insurer pays $14 million.
Situation (ii): Treaty B applies first and pays the $20 million in excess of $15 million, since the loss is above $35 million. Of the remaining $20 million, Treaty A pays 65% or $13 million, leaving (40 – 20 – 13) million = $7 million for the primary insurer.
Situation (ii) is preferable for the primary insurer.
See other sections of The Actuary’s Free Study Guide for Exam 6.