1. Alpha Insurance is a property and liability insurer that enters into a surplus-share reinsurance treaty with Strongoak Re as the 1st surplus and Lastresort Re as the 2nd surplus. Alpha has a retention limit of $200,000 on any single building, and up to 3 lines of insurance are ceded to Strongoak Re and up to 4 lines of insurance are ceded to Lastresort Re. Alpha Insurance also writes a substantial amount of commercial liability insurance as well. Alpha has a reinsurance contract with Bermuda Re and under the terms of the contract, Alpha Insurance covers 30% of the total coverage, pays 30% of the total losses and retains 30% of the total premium on a single commercial liability insurance policy. Bermuda Re thus covers 70% of the total coverage, pays 70% of the total losses and retains 70% of the total premium.

(a) What is the capacity (maximum amount of insurance coverage) that Alpha can write on a single building?

(b) A building valued at $1,500,000 is insured with Alpha with the full coverage. Shortly after the policy was issued, a windstorm caused a $300,000 loss to the building. How much of the loss will Alpha, Strongoak, and Lastresort pay respectively?

(c) Another building valued at $500,000 is also insured with Alpha with the full coverage. Likewise, shortly after the policy was issued, a fire incident caused a $10,000 loss to the building. How much of the loss will Alpha, Strongoak, and Lastresort pay respectively?

(d) What type of reinsurance contract best describes the reinsurance arrangement that Alpha Insurance has with Bermuda Re?

(e) A large pharmaceutical company requests $80 million coverage of liability insurance with Alpha Insurance to cover its business operations and is approved. If a $60 million covered loss occurs, how much will Alpha Insurance and Bermuda Re have to pay respectively?

(f) Suppose Alpha Insurance switched the current treaty with Bermuda Re to an excess-of-loss treaty, with Alphas retention limit as $10 million, and Bermuda takes up to 9 lines, what is the capacity that Alpha can write on a single liability insurance policy? Under this scenario, perform the same calculations in (e).