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Rough descriptions of ruin for a general class of surplus processes. (English) Zbl 0932.60046
Let \(\{Y_n, n\geq 1\}\) be a stochastic process and \(M\) a positive real number. One can interpret \(-Y_n\) as the accumulated surplus and \(M\) as the initial capital of an insurance company. Define the time of ruin by \(T= \inf\{n: Y_n>M\}\) (\(T=+\infty\) if \(Y_n\leq M\) for \(n=1,2,\dots\)). Using the techniques of large deviations theory the author obtains rough exponential estimates for ruin probabilities for a general class of processes. He also generalizes the concept of the safety loading and considers its importance to ruin probabilities.

60G40 Stopping times; optimal stopping problems; gambling theory
60F10 Large deviations
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