On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes

2016/08/31 by Dmitry Korshunov, Korshunov, Dmitry · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60F10 #60G51 #60K05 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #math.PR #msc:60F10 #msc:60G51 #msc:60K05

paper · pdf · doi:10.48550/arxiv.1608.09004

openalex publication_date 2016/08/31 · arxiv created 2016/11/20 · arxiv updated 2016/11/22 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study subexponential tail asymptotics for the distribution of the maximum M_t:=sup_u∈[0,t]X_u of a process X_t with negative drift for the entire range of t>0. We consider compound renewal processes with linear drift and Lévy processes. For both we also formulate and prove the principle of a single big jump for their maxima. The class of compound renewal processes particularly includes Cramér-Lundberg risk process.

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