Risk Management Steps, the Law of Large Numbers, Types of Insurers, and Insurance Functions: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Insurance Operations, Regulation, and Statutory Accounting, 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:

Myhr, A.E.; and Markham, J.J. Insurance Operations, Regulation, and Statutory Accounting (Second Edition). American Institute for Chartered Property Casualty Underwriters.

2004. Chapter 1, pp. 1.3-1.11, 1.26-1.31.

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

Problem S5-47-1. Six steps in the risk management process are mentioned by Myhr and Markham, p. 1.5:

1. Identify loss exposures.
2. Analyze loss exposures.
3. Examine the feasibility of risk management techniques.
4. Select the most appropriate techniques.
5. Implement the risk management techniques.
6. Monitor results and make changes as needed.

Business X is implementing a risk management process. The following steps (not necessarily in sequence) have been taken by employees of Business X. Match each situation below to the corresponding step in the risk management process.

(a) The management of Business X decides that the risk of falling anvils will be controlled by putting an extremely thick rubber padding over the roof of the business's main office, while the risk of infestation by worms wearing ninja costumes will be controlled by installing automatic spray-painting devices that would paint any ninja costume pink and cause any malicious worms to cower away in shame.
(b) The risk management department of Business X conducts a detailed study of expected losses from falling anvils and worms wearing ninja costumes.
(c) During the course of six months, Business X installs rubber padding over the roof of its main office to protect against falling anvils and also installs an automatic spray-painting system to deter worms who wear ninja costumes.
(d) Inspectors hired by Business X determine that it stands to suffer the most losses from falling anvils and from infestation by worms wearing ninja costumes.
(e) After collecting data for a year, analysts from Business X determine that the rubber padding recently installed over the roof of its main office helped neutralize 85% of all falling anvils, but branch offices were still subject to roughly the same amount of falling anvil damage. The management of Business X decides to also install rubber padding on the roofs of branch offices. It has also been determined that worms wearing ninja costumes are deterred by pink spray paint only 50% of the time, whereas competitors who have used neon orange spray paint managed to get a 70% success rate. The management of Business X decides to try neon orange spray paint next year.
(f) Business X commissions studies to compare and contrast the effects of five alternative risk management techniques that have been suggested to prevent and reduce losses due to falling anvils and infestation by worms wearing ninja costumes.

Solution S5-47-1.

Situation (a) is an example of step 4: selecting the most appropriate techniques.
Situation (b) is an example of step 2: analyzing loss exposures.
Situation (c) is an example of step 5: implementing the risk management techniques.
Situation (d) is an example of step 1: identifying loss exposures.
Situation (e) is an example of step 6: monitoring results and make changes as needed.
Situation (f) is an example of step 3: examining the feasibility of risk management techniques.

Problem S5-47-2. Actuary Ω decides to develop rates for automobile insurance on the basis of the following data:
- 63 colonists driving moon rovers in calendar year 2060 have experienced an average annual cost of losses of $3500 per driver.

- 12 drivers of sport utility vehicles in Taiwan in calendar year 2031 have experienced an average annual cost of losses of $3500 per driver.

- 14 operators of wheelbarrows in California in calendar year 2055 have experienced an average annual cost of losses of $3500 per wheelbarrow operator.

Actuary Ω alleges that, on the basis of the law of large numbers, he can reasonably assume that the average cost for the drivers insured by Insurance Company Y will be $3500 per year per driver. In what manner has he misapplied the law of large numbers?

Solution S5-47-2. This question is based on the discussion in Myhr and Markham, p. 1.5, where the law of large numbers is defined as a "mathematical principle stating that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes (losses) also increases." The exposure units analyzed by Actuary Ω are probably independent, but they are far from being similar. Drivers of moon rovers are not comparable to operators of wheelbarrows in California, and the years from which the data were taken differ considerably as well. The $3500 average annual per-driver loss from the three groups of drivers is thus much more likely to be a result of coincidence than information that can be relied on to make future projections.

Problem S5-47-3. Myhr and Markham, pp. 1.6-1.10, discuss the following different types of insurers:

1. Stock insurance companies
2. Lloyd's
3. Insurance exchanges
4. Mutual insurance companies
5. Reciprocal exchanges
6. Fraternal organizations
7. Pools
8. Government insurers

Each of the following is an attribute unique to one of these types of insurers and explicitly discussed by Myhr and Markham, pp. 1.6-1.10. Match each attribute to the type of insurer to which it pertains.

(a) The policyholders of these entities elect a board of directors that appoints officers to manage the company.
(b) One of these entities is the principal provider of flood insurance in the United States.

(c) These nonprofit entities are owned by its policyholders and managed by an attorney-in-fact, which can be a for-profit organization.
(d) These entities combine a lodge or social function with their insurance function.
(e) These entities are owned by their stockholders, who elect a board of directors to oversee the company's operations.
(f) These entities consist of several insurers, not otherwise related, that join together to insure loss exposures that individual insurers are unwilling to insure.
(g) Members of these entities belong to syndicates and delegate day-to-day operations to the syndicate manager.

(h) All of the insurance pertaining to this entity is written on behalf of individual members, whose personal fortunes back the insurance.

Solution S5-47-3.

(a) pertains to 4. Mutual insurance companies.
(b) pertains to 8. Government insurers.
(c) pertains to 5. Reciprocal exchanges.
(d) pertains to 6. Fraternal organizations.
(e) pertains to 1. Stock insurance companies.
(f) pertains to 7. Pools.
(g) pertains to 3. Insurance exchanges.
(h) pertains to 2. Lloyd's.

Problem S5-47-4. Myhr and Markham, pp. 1.26-1.29, discuss the following functions of insurers:

1. Marketing
2. Underwriting
3. Claims
4. Loss control
5. Reinsurance
6. Actuarial
7. Investments
8. Information technology

Each of the following is a description that pertains primarily to one of the functions above and is explicitly discussed by Myhr and Markham, pp. 1.26-1.29. Match each description to the function to which it pertains.

(a) Calculating insurance rates, developing rating plans, and estimating loss reserves;
(b) Determining whether applications received meet the insurer's guidelines;
(c) Providing the infrastructure that supports the insurer's internal and external communications, as well as its rating, statistical, and claim payment functions;
(d) Transferring to another entity some of the insurer's potential financial consequences of certain loss exposures;
(e) Informing potential consumers about the insurer's products and services;
(f) Facilitating improved loss prevention and loss reduction;
(g) Earning returns on policyholders' premiums before the premium money is used to pay for losses;
(h) Fulfilling the insurer's contractual promises to policyholders.

Solution S5-47-4.

(a) is primarily an example of the actuarial function (6).
(b) is primarily an example of the underwriting function (2).
(c) is primarily an example of the information technology function (8).
(d) is primarily an example of the reinsurance function (5).
(e) is primarily an example of the marketing function (1).
(f) is primarily an example of the loss control function (4).
(g) is primarily an example of the investments function (7).
(h) is primarily an example of the claims function (3).

Problem S5-47-5. Myhr and Markham, pp. 1.30-1.31, discuss common ways in which the actuarial department of an insurer needs to interact with other departments. Describe some of possible ways in which the actuarial department would work with each of the following departments:
(a) Underwriting
(b) Marketing
(c) Claims

Solution S5-47-5.

(a) The actuarial department may work with the underwriting department in preparing the insurance rates and rating plans that the underwriting department subsequently uses and in preparing statistical information used to evaluate the underwriting department's performance. (Myhr and Markham 2004, pp. 1.30-1.31).

(b) "In determining rates and rating plans, the actuarial department must also consider the views of the marketing department about the acceptability of rates in the marketplace" (Myhr and Markham 2004, pp. 1.30-1.31).

(c) "The actuarial department is responsible for developing loss reserves for the insurer's Annual Statement. Consequently, it must maintain contact with the claim department, because the case reserves that the claim department establishes are an important element in establishing statement reserves" (Myhr and Markham 2004, pp. 1.30-1.31).

Other answers are possible, depending on the structure and functions of various insurers.

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