A group dental policy has a negative binomial claim count distribution with mean 300 and variance 800.

Ground-up severity is given by the following table:

Severity	Probability
40	0.25
80	0.25
120	0.25
200	0.25

You expect severity to increase 50% with no change in frequency. You decide to impose a per claim deductible of 100.

Calculate the expected total claim payment after these changes.

• Less than 18,000
• At least 18,000, but less than 20,000
• At least 20,000, but less than 22,000
• At least 22,000, but less than 24,000
• At least 24,000

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: D

Severity after increase	Severity after increase and deductible
60	0
120	20
180	80
300	200

Expected payment per loss = 0.25(0) +0.25(20) + 0.25(80) + 0.25(200) = 75

Expected payments = Expected number of losses x Expected payment per loss = 300(75) = 22,500

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.