Measures of risk for the classical risk process using saddlepoint approximation techniques

Abstract

Focussing on the classical Cramér-Lundberg risk process, the main goal of this work is to provide an evaluation method for the insurer risk due to ruin over an infinite time horizon. In analogy to the well-known value of risk and tail value of risk, Gatto and Baumgartner [1] suggest the risk measures value at ruin and tail value at ruin for risk processes with additional Wiener perturbation as well as saddlepoint approximations to those risk measures. Since the special case with no perturbation is not discussed there, this is done here using the same ideas. In essence, the saddlepoint approximation method for obtaining quantiles provided by Wang [2] is combined with saddlepoint approximation results of .