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MATH 3640 – Assignment 1
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1) (6.5 points) Recommend 3 different insurance policies to each of the below prospective
insureds:
i. A large hospital with 500 employees (doctors, nurses, physician assistants, and medical
admins)
ii. A medical manufacturing company specializing in the development of pacemakers
iii. A trucking company headquartered in Columbus, Ohio. They have a staff of 100 in the
headquarters and a large fleet of truckers in the field.
2) (2 points) Answer the following:
i. Paid Loss = 500
Ultimate Loss = 1,250
IBNR = 250
What are the Case Reserves?
ii. Incurred Loss = 500
Loss Reserve = 500
Case Reserves = 300
What is the Ultimate Loss?
3) (7 points) Using the data below, do the following:
i. Calculate the Loss Ratio for each Risk Class
ii. Calculate the overall Loss Ratio across all risks
iii. Why is the hit rate (ratio of the number of policies sold to the number of quotes) and
retention (ratio of the number or renewed policies to the number of policies up for renewal)
so high for Class D?
iv. What could the company do to improve its Loss Ratio?
Risk Class Number of Exposures Pure Premium Average Premium Hit Rate Retention
A 80 20 100 4% 65%
B 90 25 100 5% 70%
C 100 30 100 6% 75%
D 1000 110 100 90% 99%
4) (4.5 points) Using the rating manual information below, calculate the premium for a 30 year
old male with 1 prior accident. The base rate for his class is $125. He has chosen a $1,000
deductible and a limit of $200,000. He is not getting the policy for his business, so there will not
be any schedule or experience modifications.