Calculation of finite time ruin probabilities for some risk models

Our methodology for calculating finite time ruin probabilities is to bound the surplus process by discrete-time Markov chains; the average of the bounds gives an approximation to the ruin probability. This approach was used by the authors in a previous paper, Cardoso and Waters [Cardoso, R.M.R., Waters, H.R., 2003. Recursive calculation of finite time ruin probabilities under interest force. Insurance Math. Econ. 33 (3), 659-676], which considered a risk process with interest earned on the surplus.