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Ladder height and supremum of a random walk with applications in risk theory. (Chinese. English summary) Zbl 1199.60170

Summary: For a random walk on the real line with negative mean, we obtain a local asymptotic estimate and a tail asymptotic estimate for the distributions of ladder height and supremum for the random walk when the conditions for the exponential estimate are not satisfied. The results are applied to the Sparre Andersen model and some new results on the probability of ruin are presented.

MSC:

60G50 Sums of independent random variables; random walks
91B30 Risk theory, insurance (MSC2010)
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