On the moments of ruin and recovery times

In this paper we consider the calculation of moments of the time to ruin and the duration of the first period of negative surplus. We present a recursive method by considering a discrete time compound Poisson process used by Dickson et al. [Astin Bull. 25 (2) (1995) 153]. With this method we will also be able to calculate approximations for the corresponding quantities in the classical model. Furthermore, for the classical compound Poisson model we consider some asymptotic formulae, as initial surplus tends to infinity, for the severity of ruin, which allow us to find explicit formulae for the moments of the time to recovery.