Consider Lundbergs Model for Poisson Process with parameter 1 and Gamma claims (, ) = (3, 1). Given insurers loading 15% and reinsurers loading 30%, the insurer adopts the proportional reinsurance 0 a 1.

(a) Find minimum a such that the insurer makes profit, net of reinsurance

(b) Find De Vylder approximation formula to the probability of ultimate ruin

(c) Use (b) to find a that minimizes the probability of ruin for initial capital u =10 and provide the corresponding probability of ruin

(d) Sketch the graph of probability of ruin as a function of a.