For calculating the probability of ruin for the insurer under a proportional reinsurance scheme without a re-insurer loading factor, is the re-insurer's premium the expected re-insurer's claims cost or a portion of the insurer's premium (alpha*premium amount)?
The reinsurer's premium is usually: (1 + loading factor) × E(Z) With no reinsurer's loading factor (they'll be ruined with probability 1) then it'll just be E(Z) which from Ch4 is given by (1- alpha)E(X).
