RISK MODEL STATISTICS

Claims on a particular type of insurance policy follow a compound Poisson process with annual claim rate per policy 0.2. Individual claim amounts are exponentially distributed with mean 100. In addition, for a given claim there is a probability of 30% that an extra claim handling expense of 30 is incurred (independently of the claim size). The insurer changes an annual premium of 35 per policy. Use a normal approximation to estimate how many policies the insurer must sell so that the insurer has a 95% probability of making a profit on the portfolio in the year