On risk processes with double barriers
Keywords:risk process, ruin probability, double barriers, exponential claims
We consider risk processes with two barriers. The risk process starts with an initial capital u>0 and the two barriers are set at 0 and v(>u). We are interested in finding the probability φ(u,v) that the risk process hits the upper barrier v before 0. Both cases of positive and negative relative safety loading are considered. Explicit formulae for φ(u,v) are obtained in the case of positive safety loading and in a special case of negative safety loading when the claims are exponentially distributed. For the general case of negative safety loading an integral equation is derived for φ(u,v), similar to the classical result for the case of a single barrier at 0.