The maximum on a random time interval of a random walk with long-tailed increments and negative drift

By S. Foss, Stan Zachary. 2013

91 citations recorded by the source corpus.

We study the asymptotics for the maximum on a random time interval of a random walk with a long-tailed distribution of its increments and negative drift. We extend to a general stopping time a result by Asmussen (1998), simplify its proof, and give some converses.

Subfields: Finance, Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0a2291b8c6f387a90e711d770425f89b4cfe3d19

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In Finance

In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

Asymptotics of randomly stopped sums in the presence of heavy tails (2008, background): “Concerning the asymptotics for the maximum, it was shown in [13] (see also [12]) that the equi valenceP{Mτ > x} ∼ EτF (x) holds without any further assumptions on the tail distribut ion of τ if Eξ < 0 and under condition (37) otherwise.”
Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments (2005, background): “Proof Since F ∈ S implies F ∈ L, we can choose a positive increasing function hy of y such that hy →∞ as y →∞ , but the convergence is sufficiently slow that F( y − hy) ∼ F( y) as y →∞ (see, for example, Foss and Zachary [ 18 ]).”
Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation (2004, methodology): “8) was recently established by Foss and Zachary([14]).”
Asymptotics for Sums of Random Variables with Local Subexponential Behaviour (2003, background): “One can see that Theorem 2 gives a unified approach for obtaining (17) and (18).”