Hi, Question 5 (April 2014) asks us to calculate the smallest premium loading such that the probability of ruin in the first year is less than 10%. Aggregate claims follow a poisson process (lambda = 25) The distribution of claim amounts is given as: 50 (30%), 100 (50%) and 200 (20%) The insurer has a surplus of 240. Premiums are paid annually in advance When attempting the question - I used the equation: lambda*Mx(R) = (1+theta)*R*E+lambda - and then solved for theta. I approximated R by using Lundbergs inequality (given the probability of ruin of 10%), and treating Mx(R) as an exponential function. However, my theta value is negative(!) and clearly incorrect. I was wondering why this approach isn't feasible. The solution, however, treated S as approximating ~ N(2625, 343 750) [?]. Then using this was able to calculate theta using the tables. Thanks,
Mx(R) is the moment generating function of the claim size distribution. In this case claims are coming from a discrete distribution so it would not be feasible to calculate R in this way. Nevertheless, unless you are asked specifically for the ultimate probability of ruin, which is naturally a challenging thing to calculate and hence we need Lundberg's inequality to calculate an upper bound, then we should expect to need to calculate the mean and variance of the distribution and apply some sort of approximation (likely Normal) to calculate the probability. Hope this helps. Joe
