You have been asked to analyse claims in a small insurance portfolio. Claim amounts ('000) are assumed to follow a gamma distribution with parameters (500, 5) per policy. i) Using the following simple assumption of the number of claims each year: Pr(0 claims) = 0.5; Pr(1 claim)=0.4; Pr(2 claims) = 0.1, what is the expected claim amount for a portfolio of 100 policies? State clearly any assumptions that you make. 3 ii) Instead, the insurer assumes that claim frequency per annum is represented by a Poi(0.6) distribution. What is the expected frequency of 0 claims, 1 claim, 2 claims and more than 2 claims, and the resulting expected total claim amount in a year for a portfolio of 100 policies? 5 iii) You have now been presented with claim amounts for 25 claims made in the last 6 months of operation within the portfolio of 100 policies (File 3). Using bootstrapping, find an estimate of the expected claims in a 6-month period, together with a 95% confidence interval for this result. 8 iv) Compare the actual claim amounts against the assumed Gamma distribution, and explain whether you believe these are consistent, using statistical results. What assumptions have you made in using the actual results? 6 v) Compare the claim frequencies against the Poisson distribution given in part ii). Perform a goodness-of-fit test to confirm whether this poisson distribution assumption seems appropriate. 6 TOTAL MARKS 28 You have been asked to analyse claims in a small insurance portfolio. Claim amounts ('000) are assumed to follow a gamma distribution with parameters (500, 5) per policy. i) Using the following simple assumption of the number of claims each year: Pr(0 claims) = 0.5; Pr(1 claim)=0.4; Pr(2 claims) = 0.1, what is the expected claim amount for a portfolio of 100 policies? State clearly any assumptions that you make. 3 ii) Instead, the insurer assumes that claim frequency per annum is represented by a Poi(0.6) distribution. What is the expected frequency of 0 claims, 1 claim, 2 claims and more than 2 claims, and the resulting expected total claim amount in a year for a portfolio of 100 policies? 5 iii) You have now been presented with claim amounts for 25 claims made in the last 6 months of operation within the portfolio of 100 policies (File 3). Using bootstrapping, find an estimate of the expected claims in a 6-month period, together with a 95% confidence interval for this result. 8 iv) Compare the actual claim amounts against the assumed Gamma distribution, and explain whether you believe these are consistent, using statistical results. What assumptions have you made in using the actual results? 6 v) Compare the claim frequencies against the Poisson distribution given in part ii). Perform a goodness-of-fit test to confirm whether this poisson distribution assumption seems appropriate. 6 TOTAL MARKS 28
