Suppose that the claim size distribution of an insurance portfolio follows a Pareto distribution of the form a+1 α f(x) β = B\B+x (i) Derive a formula for the rth moment, αr, of this Pareto distribution in terms of its (r-1) th moment, αr-1. Show your steps clearly with reasons. (ii) From this expression find α3 and α4 using the known result for the mean μ of the above Pareto distribution. (You may assume that a>r, where a is one of the two parameters of the Pareto distribution).

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