Deductible (Exponential Loss) Examples (SOA Exam P – Probability – Univariate Random Variables)

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After completing this video you should be able to:

Calculate the expected value, variance, and standard deviation of both the loss random variable and the corresponding payment random variable upon the application of policy adjustments.

Example 1:
Ground-up losses, 𝑋, follow an exponential distribution with a mean of 1000. A deductible of 𝑑=100 is imposed. Determine 𝐸[〖𝑋|〗_(𝑋≥100) ]

Example 2:
The amount of a claim that an insurance company pays out follows an exponential distribution with a mean of 1000. A deductible of 100 is imposed on the policy. Determine the expected claim payment from the insurance company.

Example 3:
The amount of a claim that an insurance company pays out follows an exponential distribution with a mean of 1000. A deductible of 100 is imposed on the policy. Determine the expected claim payment from the insured.