An actuary wishes to analyse the amounts paid by a group of insurers on their respective...

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An actuary wishes to analyse the amounts paid by a group of insurers on their respective portfolios of commercial property insurance policies using the models of Empirical Bayes Credibility Theory. The actuary obtains the following information about the amounts of claim payments made and the number of policies sold for each of three different insurers. The data obtained are as follows. (6) (iii) Insurer A Insurer B Insurer C Year 1 £14.2m 163 £58.6m 4,435 £123m 16,184 Year 2 £15.8m 189 A/(₁-₁²-0.014667 Σ²2₂/(x2-x₂)² = -0.006103 ΣP3/(x3/-X3)²- = 0.003979 £63.1m Comment on your results. 4,761 £132m 17,443 Year 3 £22.7m 252 £81.0m 5,576 £161m 20,102 Analyse the data using EBCT Model 1, and calculate the expected total claim payment to be made by Insurer B in the coming year. Year 4 £19.0m Analyse the data using EBCT Model 2, and again calculate the expected payout amount for Insurer 8 in the coming year, assuming that the expected number of policies sold for the coming year for Insurer Bis 4,800. You may use the summary statistics given below, which have been calculated using the formulae and notation given in the Tables, again working in millions of pounds. Subscripts 1, 2 and 3 refer to Insurers A, B and C respectively. 199 £64.2m 4,581 £133m 18,000 R(1-x)²-5.106461 (x2-x)=0.336408 ΣB/(x-x)² = -0.292641 An actuary wishes to analyse the amounts paid by a group of insurers on their respective portfolios of commercial property insurance policies using the models of Empirical Bayes Credibility Theory. The actuary obtains the following information about the amounts of claim payments made and the number of policies sold for each of three different insurers. The data obtained are as follows. (6) (iii) Insurer A Insurer B Insurer C Year 1 £14.2m 163 £58.6m 4,435 £123m 16,184 Year 2 £15.8m 189 A/(₁-₁²-0.014667 Σ²2₂/(x2-x₂)² = -0.006103 ΣP3/(x3/-X3)²- = 0.003979 £63.1m Comment on your results. 4,761 £132m 17,443 Year 3 £22.7m 252 £81.0m 5,576 £161m 20,102 Analyse the data using EBCT Model 1, and calculate the expected total claim payment to be made by Insurer B in the coming year. Year 4 £19.0m Analyse the data using EBCT Model 2, and again calculate the expected payout amount for Insurer 8 in the coming year, assuming that the expected number of policies sold for the coming year for Insurer Bis 4,800. You may use the summary statistics given below, which have been calculated using the formulae and notation given in the Tables, again working in millions of pounds. Subscripts 1, 2 and 3 refer to Insurers A, B and C respectively. 199 £64.2m 4,581 £133m 18,000 R(1-x)²-5.106461 (x2-x)=0.336408 ΣB/(x-x)² = -0.292641

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To analyze the data using Empirical Bayes Credibility Theory EBCT we will use two different models Model 1 and Model 2 We will calculate the expected ... View the full answer