Expected total insurance claims in a month

Question

Insurance claims arrive as a Poisson process at rate 3 per day. Independently, each claim costs an average of \500. Consider a 30-day month. What is the expected total cost of claims for the month?

Accepted Answer

The month's total payout is a compound Poisson sum: a random number of claims, each of random size. Its expectation is simply the expected number of claims times the average cost per claim. The expected number of claims in 30 days is E[N] = \lambda t = 3 	imes 30 = 90. Each costs \500 on average, so E[	ext{total cost}] = E[N] 	imes E[	ext{cost}] = 90 	imes 500 = 45{,}000. Plainly: about 90 claims are expected, each worth about \500, for roughly 45{,}000 total. Takeaway. Expected aggregate loss equals (expected claim count) times (average claim size), the backbone of insurance pricing.

Expected total insurance claims in a month

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