This practice problem set is to reinforce the 3part discussion on insurance payment models (Part 1, Part 2 and Part 3). The practice problems in this post are additional practice problems in addition to Practice Problem Set 7 and Practice Problem Set 8.
Practice Problem 9A 
Losses follow a distribution that is a mixture of two equally weighted Pareto distributions, one with parameters and and the other with with parameters and . An insurance coverage for these losses has an ordinary deductible of 1000. Calculate the expected payment per loss. 
Practice Problem 9B 
Losses, prior to any deductible being applied, follow an exponential distribution with mean 17.5. An insurance coverage has a deductible of 8. Inflation of 15% impacts all claims uniformly from the current year to next year.
Determine the percentage change in the expected claim cost per loss from the current year to next year. 
Practice Problem 9C 
Losses follow a distribution that has the following density function.
An insurance policy is purchased to cover these losses. The policy has a deductible of 3. Calculate the expected insurance payment per payment. 
Practice Problem 9D 
Losses follow a distribution with the following density function.
An insurance coverage pays losses up to a maximum of 100,000. Determine the average payment per loss. 
Practice Problem 9E 
You are given the following information.
Determine the average insurance payment per loss. 
Practice Problem 9F 
You are given the following information.
Determine the proportion of the losses that exceed 1,000. 
Practice Problem 9G 
Losses follow a uniform distribution on the interval . The insurance coverage has a deductible of 250. Determine the variance of the insurance payment per loss. 
Practice Problem 9H 
Losses follow an exponential distribution with mean 500. An insurance coverage that is designed to cover these losses has a deductible of 1,000. Determine the coefficient of variation of the insurance payment per loss. 
Practice Problem 9I 
Losses are modeled by an exponential distribution with mean 3,000. An insurance policy covers these losses according to the following provisions.
Determine the expected insurance payment per loss. 
Practice Problem 9J 
You are given the following information.
Determine the insurance company’s expected claim cost per claim after the effective date of the reinsurance policy. 
Problem  Answer 

9A 

9B 

9C 

9D 

9E 

9F 

9G 

9H 

9I 

9J 

Daniel Ma actuarial
Dan Ma actuarial
2017 – Dan Ma