Suppose that x is exponentially distributed and for a

Question

1. Suppose that the severity distribution changes from X to (1 + r)X due to inflation.

(a) Show that if the deductible d is increased to (1 + r)d, the LER is unchanged. What happens to the LER if d is unchanged?

(b) Suppose that X is exponentially distributed and for a certain value of d the LER is 0.3. If r = 0.10 and d is unchanged, what is the new LER?

2. Suppose that N is a continuous mixture of Poisson(λ) distributions, where λ ∼γ (2, 1) and X takes the value 1 with probability 0.6 and 2 with probability 0.4. If f_S(10) = c and f_S(11) = d, find a formula for f_S(12) in terms of c and d.