Your company practices all available safety and quyality control protocols of your global industry. Yet accidental or fortuitous events causing harm still occur. You are facing such an event in your firm, and furthermore the event is low frequency, high severity. The claims per event average $$100$ and the standard deviation of these claims is $$10.$ In talking to other managers of firms in your industry you discover that they are also exposed to the identical event. There is a total of $1,000$ such events globally.

$($a$)$ If you form an association captive, how much of a reserve will the captive insurer need to have, to pay almost all of the claims from these events? $($Hint: Consider information in chapter $2.)$

$($b$)$ In this situation, is the use of a captive insurer an appropriate risk management technique for this event? $($Hint: Consider information in chapter $3$ and chapter $5.)$