Answer the four questions

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Chapter 6

2. Liability Insurance Company writes a substantial amount of commercial liability insurance. A large construction company requests $100 million of liability insurance to cover its business operations. Liability Insurance has a reinsurance contract with Bermuda Re that enables the coverage to be written immediately. Under the terms of the contract, Liability Insurance pays 25 percent of the losses and retains 25 percent of the premium. Bermuda Re pays 75 percent of the losses and receives 75 percent of the premium, less a ceding commission that is paid to Liability Insurance. Based on the preceding, answer the following questions:

a What type of reinsurance contract best describes the reinsurance arrangement that Liability Insurance has with Bermuda Re?

b If a $50 million covered loss occurs, how much will Bermuda Re have to pay? Explain your answer.

c Why does Bermuda Re pay a ceding commission to Liability Insurance?

Chapter 7

4. For the past calendar year, a property insurer reported the following financial information for a specific line of insurance:

Premiums written


Expenses incurred


Incurred losses and   loss-adjustment expenses


Earned premiums


a What was the insurer’s loss ratio for this line of coverage?

b Calculate the expense ratio for this line of coverage.

c What was the combined ratio for this line of coverage?


Chapter 6

Reinsurance can be used by an insurer to solve several problems. Assume you are an insurance consultant who is asked to give recommendations concerning the type of reinsurance plan or arrangement to use. For each of the following situations, indicate the type of reinsurance plan or arrangement that the ceding insurer should use, and explain the reasons for your answer.

a Company A is an established insurer and is ­primarily interested in having protection against a catastrophic loss arising out of a single occurrence.

b Company B is a rapidly growing new company and desires a plan of reinsurance that will reduce the drain on its surplus because of the expense of writing a large volume of new business.

c Company C has received an application to write a $50 million life insurance policy on the life of the chief executive officer of a major corporation. Before the policy is issued, the underwriter wants to make certain that adequate reinsurance is available.

d Company D would like to increase its underwriting capacity to underwrite new business.

Chapter 7

Carolyn is senior vice president of finance and chief actuary for Rock Solid Insurance Company (RSIC). Lonnie is double-majoring in finance and mathematics at State University. Lonnie applied for an internship with Rock Solid, and he is working for the company during the summer before the start of his senior year of college. Curious to learn what Lonnie knew about insurance company financial statements and ratemaking, Carolyn prepared a quiz for Lonnie to take on his first day on the job. See if you can help Lonnie answer these questions.

1 At year-end last year, Rock Solid had total liabilities of $640 million and total assets of $900 million. What was the company’s policyholders’ surplus?

2 Explain how it is possible for Rock Solid to have $500 million in written premiums last year and $505 million in earned premiums last year.

3 Rock Solid’s net underwriting result last year was a $540,000 loss. Explain how it is possible that Rock Solid was required to pay income taxes.

4 Rock Solid provides collision coverage for 1 year on 50,000 autos located in a specific territory within the state. During the 1-year period, the company expects to pay $10 million in incurred losses and loss-adjustment expenses for these 50,000 autos. Based on this information, what is the pure premium?

5 The pure premium per unit of personal liability insurance for one group of prospective purchasers is $300. If Rock Solid wants to allow for a 40 percent expense ratio for this line of coverage, what gross rate per unit of coverage should be charged?

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