The effect of interest on negative surplus

In the classical continuous time surplus process, we allow the process to continue if the surplus falls below zero. When the surplus is below zero, we assume that the insurer borrows any sum of money required to pay claims, and pays interest on this borrowing. We use simulation to study moments and distributions of three quantities: the time to recovery to surplus level zero, the number of claims that occur when the surplus is below zero, and the maximum absolute value of the surplus process when it is below zero. We also show how simulation can be used to estimate the probability of absolute ruin.