The supremum of a negative drift random walk with dependent heavy-tailed steps

By Thomas Mikosch, Gennady Samorodnitsky. 2000

138 citations recorded by the source corpus.

Subfields: Finance, Management Information Systems, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/60485dfb3d2be7e3ca6f2ff2384c68d13d962ead

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Citations in the corpus

A ruin model with dependence between claim sizes and claim intervals (2004, unknown): “For heavy-tailed claim size distributions, the asymptotic behaviour of the ruin probability with dependent claims was studied e.g. in Asmussen et al. [5] and Mikosch and Samorodnitsky [9, 10].”
Copulas: Tales and facts (2006, background): “In the case of regularly varying tails for linear processes (including ARMA) under the weakest possible conditions, see Mikosch and Samorodnitsky [20], and Basrak et al.”
Ruin probability with claims modeled by a stationary ergodic stable process (2000, background): “However, this process is just an AR(1) linear process, and it follows from the general result of Mikosch and Samorodnitsky (1998) that for this process (u) C 2 ( 1) e 1 (e 1) 1 u ( 1) = C 2( 1) I(f) ; u!1 ; and so (4.”
Measures of serial extremal dependence and their estimation (2013, background): “Stable processes with infinite variance have become popular due to their attractive theoretical and modeling properties; see Samorodnitsky and Taqqu [64].”
Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables (2009, unknown): “Mikosch and Samorodnitsky [23, 24], Korshunov et al.”
Regularly varying functions (2006, result): “The following conditions from Mikosch and Samorodnitsky [41] are best possible in the sense that the conditions on (ψ i ) coincide with or are close to the conditions in the 3-series theorem.”
Asymptotics for Weighted Random Sums (2011, methodology): “Deterministic, real-valued weights with the {Xi} in R−α were considered in [16].”
Ruin theory revisited: stochastic models for operational risk (2002, background): “A solution to this problem is presented in Embrechts and Samorodnitsky [31] through a combination of the “one large claim heuristics” and the notion of operational time (time change).”
Tail probabilities for infinite series of regularly varying random vectors (2007, methodology): “This follows from Mikosch and Samorodnitsky (2000) in the case d = p = 1; the extension to the vector case is immediate.”