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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.

##### MSC:
 60G40 Stopping times; optimal stopping problems; gambling theory 60F10 Large deviations
##### Keywords:
large deviations theory; ruin problem
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