Question

ABC Insurance Company is considering to buy reinsurance from 123 Re. There are two

types of agreement they have in mind: quota share treaty or surplus share treaty. Consider

the two policies (lines) and answer the following questions under the two types of terms of

the agreement.

Policy A insures Building A for $10,000 for a premium of $300, with one loss of $5,000.

Policy B insures Building B for $12,000 for a premium of $350, with one loss of $4,000.

a. Under a quota share treaty with a $250,000 limit, a retention of 40%, and a cession of

60%, what are the amount of insurance, premiums, and losses ABC Insurance Company

is responsible for the two policies?

b. Under a surplus share treaty where ABC retains a line of $10,000 and a maximum ces-

sion of $225,000, what are the amount of insurance, premiums, and losses 123 Re is

responsible for the two policies?

Answer 1

1. Quota Share Treaty

Policy A

Risk sharing = ABC Insurance Company retains 40% i.e. $10,000 *40% = $ 4,000 and 123 Re will cede 60% i.e. $ 10,000 * 60% = $ 6,000

Premium Sharing = ABC Insurance Company retains 40% i.e. $ 300 *40% = $ 120 and 123 Re will cede 60% i.e. $ 300 * 60% = $ 180

Loss Sharing = ABC Insurance Company retains 40% i.e. $ 5,000 *40% = $ 2,000 and 123 Re will cede 60% i.e. $ 5,000 * 60% = $ 3,000

Policy B

Risk sharing = ABC Insurance Company retains 40% i.e. $12,000 *40% = $ 4,800 and 123 Re will cede 60% i.e. $ 12,000 * 60% = $ 7,200

Premium Sharing = ABC Insurance Company retains 40% i.e. $ 350 *40% = $ 140 and 123 Re will cede 60% i.e. $ 350 * 60% = $ 210

Loss Sharing = ABC Insurance Company retains 40% i.e. $ 4,000 *40% = $ 1,600 and 123 Re will cede 60% i.e. $ 4,000 * 60% = $ 2,400

2. Surplus Share Treaty

ABC retention                 $ 10,000

Treaty receives                $ 225,000

                                        $ 235,000

Policy A

Risk sharing = ABC will pay $ 10,000 pays, 123 Re pays nothing

Premium Sharing = ABC will pay $ 300, 123 Re pays nothing

Loss sharing = ABC will pay $ 5,000, 123 Re pays nothing

Policy B

Risk sharing = ABC will pay $ 10,000 (83.33%) pays, 123 Re pays $ 2,000 (16.67%)

Premium Sharing = ABC will pay $ 292, 123 Re pays $ 58

Loss sharing = ABC will pay $ 3,333, 123 Re pays $ 667