TheW,Zscale functions kit for first passage problems of spectrally negative Lévy processes, and applications to control problems

DOI10.1051/ps/2019022zbMath1461.60028arXiv1706.06841OpenAlexW2676108997MaRDI QIDQ5135954

Danijel Grahovac, Florin Avram, Ceren Vardar-Acar

Publication date: 24 November 2020

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.06841

zbMATH Keywords

capital injectionsscale functionsGerber-Shiu functionsdividend optimizationspectrally negative processesgeneralized drawdown stoppingParisian observationsprocesses with PoissonianSkorokhod regulation

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stopping times; optimal stopping problems; gambling theory (60G40) Probabilistic potential theory (60J45)

Related Items (11)

Unified approach for solving exit problems for additive-increase and multiplicative-decrease processes ⋮ An optimal stopping problem for spectrally negative Markov additive processes ⋮ On q-scale functions of spectrally negative Lévy processes ⋮ Moments of the ruin time in a Lévy risk model ⋮ On moments of downward passage times for spectrally negative Lévy processes ⋮ A scale function based approach for solving integral-differential equations in insurance risk models ⋮ Fluctuation theory for one-sided Lévy processes with a matrix-exponential time horizon ⋮ First passage problems for upwards skip-free random walks via the scale functions paradigm ⋮ Maximum drawdown and drawdown duration of spectrally negative Lévy processes decomposed at extremes ⋮ On scale functions for Lévy processes with negative phase-type jumps ⋮ General drawdown of general tax model in a time-homogeneous Markov framework

Uses Software

• Mathematica
• SpectrallyNegativeMarkovAdditiveProcess

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