An asymptotic expression for the probability of ruin within finite time
The author derives asymptotic expressions for the probability that a two- dimensional random walk crosses the ordinate y for the first time to the left of the abscissa x, as x and y tend to \(\infty\). Two applications are given, a large deviation result for the maximum of a one-dimensional random walk and asymptotic expressions for the distribution of the time of ruin in a risk reserve process.
scientific article; zbMATH DE number 4153622