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.
Publié le : 1990-01-14
Classification:
Random walk,
boundary crossing,
large deviations,
60J15,
60F10
@article{1176990954,
author = {Hoglund, Thomas},
title = {An Asymptotic Expression for the Probability of Ruin within Finite Time},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 378-389},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990954}
}
Hoglund, Thomas. An Asymptotic Expression for the Probability of Ruin within Finite Time. Ann. Probab., Tome 18 (1990) no. 4, pp. 378-389. http://gdmltest.u-ga.fr/item/1176990954/