Occurrence-Based Versus Claims-Made Insurance Policies: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Basic Ratemaking, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. 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.

Source:
Werner, Geoff and Claudine Modlin. Basic Ratemaking. Casualty Actuarial Society. 2009. Chapter 16, pp. 306-315.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S5-121-1. Werner and Modlin, p. 308, discuss five principles of claims-made insurance policies. Fill in the blanks in the following statements pertaining to each of these principles:

(a) If claim costs are increasing, a claims-made policy should cost ______ (more, less, the same, sometimes more and sometimes less) than an occurrence policy.

(b) Suppose that underlying trends in claim costs have suddenly and unexpectedly changed. Then the claims-made policy based on the prior trend will be _____ (more, less, just as, sometimes more and sometimes less) reflective of the correct price than an occurrence policy based on the prior trend.

(c) Suppose that the reporting pattern for claims has shifted suddenly and unexpectedly. The cost of a mature claims-made policy will be (more, less, just as, sometimes more and sometimes less) ______ affected than an occurrence policy.

(d) Claims-made policies have ______ (higher, lower, the same, sometimes higher and sometimes lower) risk of reserve inadequacy, compared to occurrence policies.

(e) These is _____ (more, less, the same, sometimes more and sometimes less) investment income earned by the insurer under claims-made policies, as compared to occurrence policies.

Solution S5-121-1. The following answers are in accord with the principles stated by Werner and Modlin, p. 308:

(a) If claim costs are increasing, a claims-made policy should cost less than an occurrence policy.

(b) Suppose that underlying trends in claim costs have suddenly and unexpectedly changed. Then the claims-made policy based on the prior trend will be more reflective of the correct price than an occurrence policy based on the prior trend.

(c) Suppose that the reporting pattern for claims has shifted suddenly and unexpectedly. The cost of a mature claims-made policy will be less affected than an occurrence policy.

(d) Claims-made policies have lower risk of reserve inadequacy, compared to occurrence policies.

(e) These is less investment income earned by the insurer under claims-made policies, as compared to occurrence policies.

Problem S5-121-2. Dr. □ had an occurrence-based medical malpractice insurance policy from January 1, 2013 to December 31, 2018. Immediately thereafter, Dr. □ purchased a claims-made policy.

The following medical malpractice claims were made against Dr. □:

Claim A was reported on January 4, 2015, because of an incident that occurred on May 6, 2013.
Claim B was reported on October 7, 2016, because of an incident that occurred on December 14, 2015.
Claim C was reported on August 15, 2019, because of an incident that occurred on January 7, 2016.
Claim D was reported on September 20, 2020, because of an incident that occurred on April 29, 2018.
Claim E was reported on July 11, 2021, because of an incident that occurred on May 30, 2020.
Claim F was reported on July 1, 2022, because of an incident that occurred on February 3, 2013.

(a) For which of these claims is there coverage overlap between the occurrence policy and the claims-made policy?

(b) The insurer writing the claims-made policy can set a retroactive date that would eliminate coverage overlaps. What should be the retroactive date for this policy?

Solution S5-121-2. This problem is based on the discussion in Werner and Modlin, pp. 311-312.

(a) Coverage overlaps exist for all claims that were reported after December 31, 2018, but for which the incidents occurred before December 31, 2018. This means that Claims C, D, and F are subject to coverage overlap.

(b) The retroactive date is the date on or after which an incident must have occurred in order to be eligible for coverage under a claims-made policy. To eliminate coverage overlaps, the insurer should set the retroactive date to the first day on which the occurrence policy was no longer in effect: January 1, 2019.

Problem S5-121-3. An insurer writing claims-made policies employs step factors pertaining to insureds who have recently obtained the policies.

For the first claims-made year, the factor is 0.2.
For the second claims-made year, the factor is 0.5.
For the third claims-made year, the factor is 0.6.
For the fourth claims-made year, the factor is 0.8.
For the fifth claims-made year, the factor is 0.98.

For the sixth claims-made year and every year thereafter, the factor is 1.00.

(a) Based on the step factors above, what is the fraction of the cost of a mature claims-made policy that the insurer estimates to be based on costs of claims pertaining to the year three years before the year for which the policy was issued?

(b) Based on the step factors above, what is the fraction of the cost of a mature claims-made policy that the insurer estimates to be based on costs of claims pertaining to the time period starting four years before the year for which the policy was issued and ending two years before the year for which the policy was issued?

Solution S5-121-3. This problem is based on the discussion in Werner and Modlin, p. 313.

(a) The step factor for the first claims-made year is also the factor pertaining to the insurer's estimates of costs for the current year of the policy. The step factor for the nth claims-made year is also the factor pertaining the insurer's estimates of costs for the time period from (n-1)st year prior to the current year of the policy to the current year of the policy. Thus, the following are true:

Factor for current year cost: 0.2
Factor for current and prior year cost: 0.5
Factor for prior year cost: 0.5 - 0.2 = 0.3
Factor for current and prior and 2^nd-prior year cost: 0.6
Factor for 2^nd-prior year cost: 0.6 - 0.5 = 0.1
Factor for current and prior and 2^nd-prior and 3^rd-prior year cost: 0.8
Factor for 3^nd-prior year cost: 0.8 - 0.6 = 0.2

(b) By the reasoning in part (a), the factor for the cost of the current year through the 4^th-prior year is 0.98. The factor for the current and prior year cost is 0.5. The difference between the two is the desired factor representing cost of a mature claims-made policy that the insurer estimates to be based on costs of claims pertaining to the time period starting four years before the year for which the policy was issued and ending two years before the year for which the policy was issued: 0.98 - 0.5 = 0.48.

Problem S5-121-4. Dr. ◊ is an otherwise identical version of Dr. □, except that, instead of switching from an occurrence-based policy to a claims-made policy, Dr. ◊ switched from a claims-made policy to an occurrence-based policy. He had a claims-made medical malpractice insurance policy from January 1, 2013 to December 31, 2018. Immediately thereafter, Dr. ◊ purchased an occurrence-based policy.

The following medical malpractice claims were made against Dr. ◊:

Claim A was reported on January 4, 2015, because of an incident that occurred on May 6, 2013.
Claim B was reported on October 7, 2016, because of an incident that occurred on December 14, 2015.
Claim C was reported on August 15, 2019, because of an incident that occurred on January 7, 2016.
Claim D was reported on September 20, 2020, because of an incident that occurred on April 29, 2018.
Claim E was reported on July 11, 2021, because of an incident that occurred on May 30, 2020.
Claim F was reported on July 1, 2022, because of an incident that occurred on February 3, 2013.

(a)For which of these claims would there be a coverage gap due to the switch in policies?

(b) What could Dr. ◊'s new insurer do to eliminate the coverage gap?

Solution S5-121-4. This question is based on the discussion in Werner and Modlin, pp. 313-314.

(a) The coverage gap exists for claims that were reported after the expiration of the claims-made policy but pertain to incidents occurring prior to the effective date of the occurrence policy. Thus, the claims-made policy no longer provides coverage for these claims, and they are also not encompassed within the occurrence period of the occurrence policy. All claims for incidents that occurred before January 1, 2019, but were reported after January 1, 2019, fall into this category. Thus, there are coverage gaps for Claims C, D, and F.

(b) To eliminate the coverage gaps, the new insurer can provide Dr. ◊ with an extended reporting period endorsement that offers "tail coverage" for claims that are reported during the time period of the occurrence policy but pertain to incidents that occurred before the occurrence policy took effect.

Problem S5-121-5. Suppose an insurer decides to switch from writing occurrence-based policies to writing claims-made policies. Briefly explain how the following would be affected:

(a) Determination of the IBNR (incurred but not reported) reserve.
(b) Determination of the IBNER (incurred but not enough reported) reserve.

Solution S5-121-5. This question is based on the discussion in Werner and Modlin, p. 311.

(a) Claims-made policies do not have an IBNR aspect, because the insurer is only responsible for claims that are reported in the year of the policy. Claims that are not reported do not apply to the year in question.

(b) It is still necessary to calculate an IBNER reserve for claims that were reported during the year of the policy, but for which the costs end up being greater than originally expected. For instance, the costs of a claim reported in year X could, as a result of a protracted lawsuit, increase far beyond the original projections - but the higher costs might not be fully apparent until year X + k, where k ≥ 1.

See other sections of The Actuary's Free Study Guide for Exam 5.