Hi, I am really stuck at understanding of section 4 'The Normal approximation to G(X), how can we have a normal approximation to the claim amount(s) which are always greater than or equal to zero. Please help me in understanding this.
If the normal distribution has a sufficiently low probability of being less than zero it may still be a useful approximation.
The fact that the Normal approximation allows negative claim amounts is one of its biggest weaknesses (along with the fact that the Normal distribution is symmetric whereas the distribution of insurance claims is typically positively skewed). Later in the chapter you will also find the Translated Gamma approximation which is an alternative that avoids some of the disadvantages of the Normal model
