Ruin probabilities with compounding assets for discrete time finite horizon problems, independent period claim sizes and general premium structure

In this paper we present fast and accurate approximations for the probability of ruin over a finite number of periods, assuming inhomogeneous independent claim size distributions and arbitrary premium income in subsequent periods. We develop exact recursive expressions for the non-ruin probabilities in subsequent periods. These recursive expressions provide the basis for a computationally efficient recursive approximation scheme based on two-moment gamma distribution fits. An extensive simulation experiment showed the accuracy ofthe approximations for values of the horizon up to 20. Especially for small values of the ruinprobability the approximations are very accurate. Having shown the validity ofthe approximations, we applied them to gain insight into two non-stationary investment problems.