Solve all the questions in the attachment.
The cumulative claims paid each year under a certain cohort of insurance policies are recorded in we the table below, for accident years 2010, 2011, 2012 and 2013. Development Year Accident Year 0 1 2 2010 2,457 4,196 4,969 5,010 2011 2,648 4,715 5,561 2012 3,084 5,315 2013 3,341 (i) Calculate the development factors under the basic chain ladder technique and state the assumptions underlying the use of this method. [4] (ii) The rate of claims inflation over these years, measured over the 12 months to the middle of each year, is given in the table below. 2011 2.1% 2012 10.5% 2013 3.2% Calculate the development factors under the inflation-adjusted chain ladder technique and state the assumptions underlying the use of this method. [6] (iii) Based on the development factors calculated in parts (i) and (ii), calculate the fitted values under these two models and comment on how these compare with the actual values. [7] [Total 17] 8 The table below shows the payments, in f'000s, made in successive development years in respect of a particular class of general insurance business. It may be assumed that all claims are fully settled by the end of Development Year 3 and that all payments are made in the middle of a calendar year. Year of origin Development Year 1 2 3 2012 342 82 68 37 2013 359 90 73 2014 481 120 2015 591Use the inflation adjusted chain ladder method to estimate the amount of the reserve required at the end of 2015 to pay the outstanding amounts in respect of claims from 2013, 2014 and 2015. You should assume that past inflation has been at the rate of 5% per annum and that future inflation will also be at 5% per annum. [10] 9 The tables below show the cumulative cost of incurred claims and the number of claims reported each year for a certain cohort of insurance policies. The claims are assumed to be fully run-off at the end of Development Year 2. Cumulative cost of incurred claims: Development Year Accident Year 1 2 288 634 893 465 980 2 773 The numbers of claims reported in each year are: Development Year Accident Year 0 1 2 0 110 85 55 167 113 N 285 Given that the total amount paid in claims to date, relating to accident years 0, 1 and 2, is $2,750, calculate the outstanding claims reserve using the average cost per claim method. [11] 10 The following table shows cumulative incurred claims data, by year of accident and reporting tyle development, for a portfolio of domestic household insurance policies: Cumulative incurred claims Development Year (EOOO) 1 2 Accident Year 2011 829 917 978 1,020 2012 926 987 1,053 2013 997 1,098 2014 1,021The corresponding cumulative number of reported claims, by year of accident and reporting development, are as follows: Cumulative number of Development Year reported claims Accident Year 2011 63 68 70 74 2012 65 69 72 2013 71 76 2014 70 Use the average cost per claim method with simple average grossing up factors to calculate an estimate of the outstanding claim amount for these policies for claims arising during these accident years. The claims paid to date are $3,640,000. State any assumptions used. [11]
