Dear All Please can i check for this question for some queries below: Where has the question mentioned clearly that we need to consider technical reserves for standard and guarantee business separately? i found the only line that tells me this is: 'For the most recent four years it has written part of its book of home contents insurance with a return of premium guarantee' 2 solution has assumed '10 /11 of the written premium relates to the standard contents policy, the other the premium guarantee.' Where is this based on? I don't find any exam info that suggest this..? or can we make any assumption, eg 2/3 is standard, so long we stick with this for our calculation throughout then we will get full marks? 3 On the last part where we find 'Estimated ultimate premium eligible for the guarantee' 2010 : 1557 = 5,938 *0.8^6 5938 are made up by written premium from policies started in 2010 which renewed in 2011,12,and 13.what about subsequent renewals after 2013? i thought the policy has to be renewed for 10 years after it is first written to qualify for the guarantee ? not sure i get why we use 5938 which is the sum of all renewals premiums but they all belong to the same set of policy? Overall i found this question to be the most complex, is there similar ones? Much appreciated! Thanks Jun
Hi Jun 1. They broke the product into its component parts ie. the home contents part and the premium guarantee part. This makes sense because the components require different reserves. 2. The question says the premium guarantee premium is 10% of the standard rates. The total premiums will be 10% plus 100% =110% of standard rates. The ratio of standard premiums and premium guarantee premiums to total premiums are 10/11 and 1/11 respectively. 3. The valuation as at end of 2013 is being done on policies in force as of that date. So you need to estimate the policies from each prior year with a guarantee at that date that will be in force at the end of 10 years. So you get the premium at risk for the policies that are still in force and project their likelihood of being in force at the end of 10 years. For the policies taken out in 2010 the probability they will be in force in 6 years' time if the lapse rate is 20% annually is 0.8^6 and they have a premium at risk of 5938. Hope that helps
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Thanks zivanaik ! Can I ask the following please : On the premium at risk - this is the amount of premium relating to 2010 policies that may be returned if they are still in force after another 6 years (looking from YE 2013)? Ok, but what about the 2010 policies renewal premium for 2014, 2015... 2019 (10th year)? They will also become at risk and in fact if we were predicting renewals for the next 6 years, do we not need to account for these 6 years of renewal premiums?
Hi Jun The 0.8^6 takes care of that. Let's take it step by step. At end of 2013 the premium at risk is 5938. At end of 2014 it will be 5938*0.8 after 20% lapse. This is the premium at risk at the start of the following year 2015. At end of 2015 the premium at risk is expected to be 5938*08*0.8 after a further 20% lapse. By the same logic at the end of the 10 years, six years from now, we expect 0.8^6 of the 5938 premium to be still present. therefore taking into account lapses you expect 5938*0.8^6 to be the premium reserve for the guarantee at the end.
Hi, Zivanaik, thanks for your input here. Spot on! Jun, I hope that all helps, do respond back if not. Thanks Aman Sehra ActEd Tutor
