Question 1: A reinsurance company writes a book of catastrophe reinsurance contracts to an expected combined ratio of 60%. This estimates that its aggregate claims distribution is compound Poisson with λ = 20% and the claim size distribution is exponential with mean of $1m.
a) Compute the minimum amount of capital it needs to make sure that its ultimate probability of ruin stays below 0.5%.
b) Ignoring investment income, compute the return on capital that the reinsurer would produce if it held the amount of capital that you computed in (a) above.
c) Propose potential practical limitations of the above solution.
Question 2: A small general insurance company (A) writing only property business cedes a quota share reinsurance arrangement to reinsurance company (B). The treaty cedes 40% of the protected portfolio. A pays 25% commission to get the business and has internal expenses of 7.5%. A expects to write £10m of business at a loss ratio of 65%. B bears the ceded proportion of A’s acquisition costs and expenses. B’s own expenses are 2% of gross premium received by B and B pays the broker 2.5% for the business.
a) Compute B’s expected profit on this treaty, stating any suppositions that you make.
b) As a pricing actuary for B you have been shown this treaty by an underwriter. Explain what changes to the treaty you might propose to the underwriter before the terms are agreed.