2018.Fall #14
In 2018.Fall #14 (https://www.battleacts8.ca/8/pdf/Exam_(2018_2-Fall)/(2018_2-Fall)_(14).pdf), where do they get the values 1.55 and 0.168 in part b? I believe the question is outdated, but I'm just curious.
One of the solutions:
Charge(Rg) = (1.65 – 1.55)/(5×0.6) = 0.04
Savings(Rh) = (0.168 – 0.15)/(5×0.6) = 0.006
I (experience) = 0.6 × (9,000,000) × (0.04 – 0.006) = 183,600
Thanks!
Comments
The question is still valid I'm afraid. It's a good application of the balance equations.
The figures you're asking about are the result of switching from working with entry ratios to working with loss ratios. Notice 1.65 = 165% which is the largest loss ratio in the table given. We can switch between entry ratios = actual loss / expected loss and loss ratios by taking this equation and multiplying it by 1 in the form standard prem / standard prem. Then we can work directly with the loss ratios as given.
Alternatively, Phi(r) is the average amount by which the known entry ratios, s_i, exceed entry ratio r. In Fisher.AggExcess we write it in terms of the number of known entry ratios and the expected loss in the denominator. That's what's happening here - the expected loss ratio is 0.6, so they're forcing the equation (2.75 - 2.55)/5 to look like (s_i-r)/(5*0.6)
Here s_i = 2.75 / 0.6 = 1.65 and y should be 1.53 = 2.55/0.6. The CAS solution has a minor typo.