Question 3 (a) An insurer has excess-of-loss reinsurance on auto insurance. You are given: Total expected losses in the year 2001 are 10,000,000. (1) (11) In the year 2001 individual losses have a Pareto distribution with F(x)=1-(+2000) .x>0 (iii) (iv) (c) (v) (vi) Calculate C2002/C2001- (b) A jewelry store has obtained two separate policies that together provide full coverage. You are given: Reinsurance will pay the excess of each loss over 3000. Each year, the reinsurer is paid a ceded premium, Cyear, equal to 110% of the expected losses covered by the reinsurance. Individual losses increase 5% each year due to inflation. The frequency distribution does not change. (1) (11) (ii) (iv) (v) The average ground-up loss is 11,100 Policy A has an ordinary deductible of 5,000 with no policy limit. Under policy A, the expected amount paid per loss is 6,500. Under policy A, the expected amount paid per payment is 10,000. Policy B has no deductible and a policy limit of 5,000. Given that a loss less than or equal to 5,000 has occurred, what is the expected payment under policy B? (1) (ii) To encourage maximum performance, your company has a profit sharing program, your bonus is based on GAAP operating earnings of the company (expressed in millions) as follows: If GAAP operating earnings are 90 or less, your bonus is 0. If GAAP operating earnings are P and P> 90, then your bonus is equal to your salary times (P-90)/100. (iii) There is no maximum for the bonus. GAAP operating earings follow a single-parameter Pareto distribution with parameter 8 -80 and a = 8. Your salary is 50,000. Calculate your expected bonus.
Question 3 (a) An insurer has excess-of-loss reinsurance on auto insurance. You are given: Total expected losses in the year 2001 are 10,000,000. (1) (11) In the year 2001 individual losses have a Pareto distribution with F(x)=1-(+2000) .x>0 (iii) (iv) (c) (v) (vi) Calculate C2002/C2001- (b) A jewelry store has obtained two separate policies that together provide full coverage. You are given: Reinsurance will pay the excess of each loss over 3000. Each year, the reinsurer is paid a ceded premium, Cyear, equal to 110% of the expected losses covered by the reinsurance. Individual losses increase 5% each year due to inflation. The frequency distribution does not change. (1) (11) (ii) (iv) (v) The average ground-up loss is 11,100 Policy A has an ordinary deductible of 5,000 with no policy limit. Under policy A, the expected amount paid per loss is 6,500. Under policy A, the expected amount paid per payment is 10,000. Policy B has no deductible and a policy limit of 5,000. Given that a loss less than or equal to 5,000 has occurred, what is the expected payment under policy B? (1) (ii) To encourage maximum performance, your company has a profit sharing program, your bonus is based on GAAP operating earnings of the company (expressed in millions) as follows: If GAAP operating earnings are 90 or less, your bonus is 0. If GAAP operating earnings are P and P> 90, then your bonus is equal to your salary times (P-90)/100. (iii) There is no maximum for the bonus. GAAP operating earings follow a single-parameter Pareto distribution with parameter 8 -80 and a = 8. Your salary is 50,000. Calculate your expected bonus.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 54E
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Transcribed Image Text:Question 3
(a) An insurer has excess-of-loss reinsurance on auto insurance. You are given:
Total expected losses in the year 2001 are 10,000,000.
(1)
(11)
In the year 2001 individual losses have a Pareto distribution with
(111)
(iv)
(c)
Each year, the reinsurer is paid a ceded premium, Cyear: equal to 110% of the
expected losses covered by the reinsurance.
Individual losses increase 5% each year due to inflation.
(vi) The frequency distribution does not change.
Calculate C2002/C2001-
(b)
A jewelry store has obtained two separate policies that together provide full coverage.
You are given:
2000
F(x)=1-(- .x>0
x+2000/
Reinsurance will pay the excess of each loss over 3000.
(1)
(11)
(iii)
(iv)
The average ground-up loss is 11,100
Policy A has an ordinary deductible of 5,000 with no policy limit.
Under policy A, the expected amount paid per loss is 6,500.
Under policy A, the expected amount paid per payment is 10,000.
Policy B has no deductible and a policy limit of 5,000.
Given that a loss less than or equal to 5,000 has occurred, what is the expected payment
under policy B?
To encourage maximum performance, your company has a profit sharing program, your
bonus is based on GAAP operating earnings of the company (expressed in millions) as
follows:
(1)
(11)
If GAAP operating earnings are 90 or less, your bonus is 0.
If GAAP operating earnings are P and P> 90, then your bonus is equal to your
salary times (P-90)/100.
(iii) There is no maximum for the bonus.
GAAP operating earnings follow a single-parameter Pareto distribution with parameter 0
= 80 and a = 8. Your salary is 50,000. Calculate your expected bonus.
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