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The matrix below shows the losses to Player A in a two player zero sum game. The strategies for Player A are denoted I. II. III and IV. Player A !I -10 -6 -3 Player B -8 -6 -3 -7 -9 (i) Determine the values of Y and Y for which there are dominated strategies for Flayer A. [4] (ii) Determine whether there exist values of X" and Y which give rise to a saddle point. [3] [Total 7] The table below shows cumulative claim amounts incurred on a portfolio of insurance policies. Accident Year Development Year 0 1 2 2011 1,509 1.969 2,106 2,207 2012 1,542 2,186 2,985 2013 1,714 1,924 2014 1,773 Annual premiums written in 2014 were 4,013 and the ultimate loss ratio has been estimated as 93.5%. Claims can be assumed to be fully run off by the end of development year 3. Estimate the total claims arising from policies written in 2014 only, using the Bornhuctter-Ferguson method. [7] (i) (a) Explain why an insurance company might purchase reinsurance. (b ) Describe two types of reinsurance. [3] The claim amounts on a particular type of insurance policy follow a Pareto distribution with mean 270 and standard deviation 340. (ii) Determine the lowest retention amount such that under excess of loss reinsurance the probability of a claim involving the reinsurer is 5%. [4] [Total 7]A shipping insurance company has insured ships for six years, and classifies the ships it insures into three types. Let: P be the number of ships insured in thejth year from type i, Y, be the corresponding number of claims. The six years of data are summarised as follows: Yiji Type (1) X. = j=1 /=1 Type 1 648 0.524 691 30 966 692 64. 192683 Type 2 981 0.145062 4.689 264 42.240804 Type 3 636 0.370 370 62.449 512 66.467 182 F = I'M I'M. = 0.297572, where P => A i-1 There are 100 ships of Type 3 to be insured in year seven. (i) Estimate the number of claims from Type 3 ships in year seven using empirical Bayes credibility theory (EBUT) Model 2. 16] The insurance company's actuary is considering using EBCT Model 1 instead. (ii) Explain an advantage and a disadvantage of using EBCT Model 1 rather than EBCT Model 2. [2] [Total 8]