Abstract
We consider quantities such as the probability that a two-dimensional random walk crosses the ordinate $y$ for the first time to the left of the abscissa $x$, and describe the asymptotic behaviour as $x$ and $y$ tend to $\infty$. The result is applied to the risk reserve process of insurance mathematics as well as to one-dimensional random walks.
Citation
Thomas Hoglund. "An Asymptotic Expression for the Probability of Ruin within Finite Time." Ann. Probab. 18 (1) 378 - 389, January, 1990. https://doi.org/10.1214/aop/1176990954
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