The exact asymptotics for hitting probability of a remote orthant by a multivariate L\'evy process: the Cram\'er case
| Autor: | Borovkov, Konstantin, Palmowski, Zbigniew |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a multivariate L\'evy process satisfying the Cram\'er moment condition and having a drift vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being translated to infinity along a fixed vector with positive components. This problem is motivated by the multivariate ruin problem introduced in F. Avram et al. (2008) in the two-dimensional case. Our solution relies on the analysis from Y. Pan and K. Borovkov (2017) for multivariate random walks and an appropriate time discretization. Comment: 7 pages, 0 figures. In the new version we fixed a bug present in the original one (the value of the constant in the main result proved to be different from the originally claimed) |
| Databáze: | arXiv |
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