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.1 The table below shows cumulative claims (not adjusted for inflation) from a portfolio of insurance policies for 4 accident years. Year of Development Year origin 1 2 3 2014 2,047 3,141 3,209 3,310 2015 2,471 3,712 3,810 2016 2,388 3,750 2017 2,580 It may be assumed that payments are made in the middle of a calendar year. It is estimated that the inflation rate applicable to these data has been 5% per annum over the relevant period. Use the inflation adjusted chain ladder method to estimate the total outstanding payments, up to the end of Development Year 3, for Accident Year 2017 in mid-2017 prices. 2 Write down an equation defining the statistical model assumed by each of the following methods of projecting the payments for outstanding claims: basic chain ladder method inflation adjusted chain ladder method Define each symbol and indicate whether the value of each quantity is assumed at the outset or is estimated by the model. 3 What does the factor xy represent in the inflation adjusted chain ladder model? A The proportion (by number) of claims paid in Development Year i+ j. B The proportion (by amount) of claims paid in Accident Year i + j. C The volume of claims for Accident Year i+ j. D An index of the cost of claims paid in calendar year i + j..4 Explain in words (ie without using mathematical symbols) the assumptions underlying the: (i) basic chain ladder method. (ii) inflation adjusted chain ladder method. (iii) average cost per claim method (iv) Bornhuetter-Ferguson method. .5 The table below shows the claim payments made by a general insurer in each year for a particular type of insurance. Claim payments made during Development Year year (EQ00s) 0 1 2 3 2012 10 50 50 30 2013 50 70 30 Accident Year 2014 40 30 2015 90 (i) What was the total amount paid during the 2015 calendar year? Calculate the development factors from development years 1 to 2 for each of the 2012 and 2013 accident years. (iii) Give three reasons why it may not be appropriate to use the basic chain ladder method to project the claim payments for this portfolio, using figures from the table to support your comments. 6 The following table shows incremental claims relating to the accident years 2007, 2008 and 2009. tyle It is assumed that claims are fully run-off by the end of Development Year 2. Estimate total outstanding claims using the chain-ladder technique, ignoring inflation. Development Year Incremental claims 0 1 2 2007 2,587 1,091 251 Accident 2008 2,053 1,298 Year 2009 3,190 [7]
