Hi, I have some questions about exposures used to compute the ultimate loss ratios under accident year basis and underwriting year basis. As far as i know, for doing the reserving of direct companies, we use accident year basis in the run-off triangle and once we have projected the ultimate losses for each accident year, we then have to divide them with earned premium of each accident year in order to get the Ultimate loss ratios. May i know why we have to use earned premiums instead of other type of premiums (say, gross premiums, net premiums etc)? When we are doing the reserving for reinsurance companies, we have to use the underwriting year basis. And we have to do a claim loss run-off triangle as well as a premium run off triangle. May i know why we have to do the premium run-off triangle for underwriting year basis? Why for underwriting year basis, we have to use the ultimate premiums as the denominators in order to get the ultimate loss ratios? Please help and explain with details and examples. Many thanks for that.
Don't get confused between gross / net (which refers to reinsurance) and earned / written (which refers to the time period we group our data into). You could use either gross earned premiums or net earned premiums when calculating an AY loss ratio. The important thing is to ensure correspondence between the premiums and claims. So, for example: AY gross claims – divide by gross earned premium AY net claims – divide by net earned premium UW year gross claims - divide by gross written premium UW year net claims - divide by net written premium It doesn’t make much sense to project earned premiums on an AY basis, because premium won’t be earned after the end of the AY. Even if you want to project premium payments by AY, it doesn’t really make sense. You wouldn’t really expect to receive premium in respect of risks that have already expired, because that would mean the insurer was covering a policyholder who hadn’t yet paid the premium. (The policyholder could in fact just have made a claim and then walked away without paying the premium.) For an underwriting year basis, it’s slightly different: Premiums can be paid over time, so they can still be received for some time after the end of the underwriting year (eg in respect of business written at the end of December say, or for pay-monthly policyholders). So a projection is useful if you want to estimate the ultimate amount received. Mind you, any projection of premium income could be useful for investment income calculations, modelling liquidity, etc. The issue here is one of correspondence again. If we project ultimate claims by UW year then the premiums need to include amounts that will be received after the end of the UW year. If we project ultimate claims by AY year then premium cannot continue to be earned after the end of the accident year. Hence we only need to talk about earned premium to date.
