Question:

A reinsurance company writes a book of catastrophe reinsurance contracts to an expected combined ratio of 60%. It estimates that its aggregate claims distribution is compound Poisson with λ=20% and the claim size distribution is exponential with mean of $1m.

a) Determine the minimum amount of capital it needs to ensure that its ultimate probability of ruin stays below 0.5%.

b) Ignoring investment income, calculate the return on capital that the reinsurer would generate if it held the amount of capital that you calculated in (a) above.

c) Suggest potential practical limitations of the above solution.