[A] What is the implied average size ($ amount) of a claim?

[B] Assuming a 20% take-up rate, so how many AI developers are covered in the insurance?

[C] Assuming a 20% take-up rate, what is the 99.5th percentile of the aggregate claims cost distribution, to the nearest thousand?

The Association of Independent Artificial Intelligence Developers (AIAID) is a trade association offering a range of services to its independent member firms. The supervisory professional body requires that every AI firm maintains professional liability insurance (PLI). An entrepreneur has decided to establish a new insurance company, New Insurance Company (NIC), to write PLI. Initially it proposes to offer insurance solely to AIAID member firms. It proposes to attract their business by ignoring their past claims experience when underwriting and by offering insurance at a substantial discount to current market rates.

The following information is provided:

AIAID Membership Information

• 300 member firms with three or fewer AI developers each. (2 on average)
• 30 member firms with 50 AI developers each.

PLI Claims Information

• 99.5% of claims cost $20,000 on average and 0.5% of claims cost $1m on average.
• On average, a group of 100 AI developers is expected to incur 8 claims in any given year.

Aggregate Claims Cost Distribution Information

• The standard deviation of the distribution is assumed to be 30% of the mean.
• The 99.5^th percentile of the distribution is assumed to be 3.5 standard deviations away from the mean.