The exact asymptotics for hitting probability of a remote orthant by a multivariate L\'evy process: the Cram\'er case

Konstantin Borovkov; Zbigniew Palmowski

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arXiv · 1802.06577

The exact asymptotics for hitting probability of a remote orthant by a multivariate L\'evy process: the Cram\'er case

Konstantin Borovkov·Zbigniew Palmowski

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Abstract

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.

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Konstantin Borovkov, Zbigniew Palmowski. 2018-02-19. The exact asymptotics for hitting probability of a remote orthant by a multivariate L\'evy process: the Cram\'er case. https://arxiv.org/abs/1802.06577

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