(*) Effect of claims inflation on various distributions. Show that applying an inflation of r% to all the losses (i.e. X X ’ = + (1 r)) modelled by:

• a Lognormal distribution with parameters µ and σ leads to a Lognormal distribution with parameters µ µ ′ ′ = + log , (1+ r) σ σ = ;

• a single-parameter Pareto distribution F x while keeping constant the threshold θ(basically, this means assuming that the Pareto distribution continues to hold below θ, at least down to a certain value) leaves the Pareto distribution unchanged;

• a GPD F x x ( ) = − +  −

while keeping constant the threshold µ leads to a GPD with parameters ξ′ ′ = = ξ σ, , σ ξ (1+ r r ) − = µ µ′ µ.