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Comments
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Study Data: Experience collected from 16 companies. Some inconsistencies were detected in the data requiring the exclusion of some records. Based on data obtained from the University of Toronto, deaths were reconciled (in numbers of policies and dollars) and the exposure (in numbers of policies and dollars) for each study year from 1997 to 2004. Methodology: The raw mortality rates were computed based on amount of insurance. These rates were calculated using the following formula: qx=Dx/(Ex) where Dx represents the total death benefits for the persons that died between age x and x+1 and where Ex represents the total exposure amounts of those insured at age x. The use of credibility theory to graduate the table was evaluated but the size of the data at various ages and duration periods was insufficient to allow the use of the methods to compute the mortality rates. Standard graduation methods were analyzed; a Whittaker-Henderson model provided the most satisfactory graduation method. The method was applied separately for Male and Female, and for the different smoking status. The Whittaker-Henderson method was used for ages up to age 80 as data was sparse at the older ages. Due to the scarcity of data at advanced ages, population mortality data was used. The method used to incorporate the population data into the insured data was adapted from the approach taken by the Society of Actuaries (SOA) to derive the VBT2008 tables (See SOA Table Identities 996-1007) The graduated ultimate mortality rates from ages 80 to 90 were made to converge linearly to the Canadian Life Tables for male and female status produced by Statistics Canada for the same observed period, with minor smoothing around age 93 to eliminate irregularities in the raw population data. After age 90, only population data is used to derive mortality rates. The omega was set to age 120, that is, q (120) = 1.00. Once the ultimate mortality rates were computed, the select rates were calculated. The relationship between the first year mortality and the ultimate mortality at the same attained age was computed. Next the parameters σ, β, φ , γ, and δ were calculated. This analysis was performed for males and females only due to lack of data for the subclasses. To complete the select tables, interpolation was done using a method devised by Panjer and Tan (1995). Once the tables were constructed, the ratio between actual and tabular death benefit was calculated. In order to have a ratio close to one, each graduated mortality table was adjusted by a factor. Finally, the inequalities for each age and duration between the smoker, non-smoker and combined rate (Non-Smoker ≤ Combined ≤ Smoker) were verified. Whenever the inequalities were not verified, the smoker or non-smoker rates were replaced by the combined rates. This was done for less than 200 values out of more than 5,000. The age nearest tables have been constructed from the age last tables using a formula due to the scarcity of age nearest data: Data Transcription Errors: None. Data Certified: 07/2013
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