Rough descriptions of ruin for a general class of surplus processes

Let {Y-n \ n = 1, 2,...} be a stochastic process and M a positive real number. Define the time of ruin by T = inf{n \ Y-n > M} (T = +infinity if Y-n less than or equal to M for n = 1, 2,...). Using the techniques of large deviations theory we obtain rough exponential estimates for ruin probabilities for a general class of processes. Special attention is given to the probability that ruin occurs up to a certain time point. We also generalize the concept of the safety loading and consider its importance to ruin probabilities.