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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 = +∞ if Y n ≤ 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.