Predicting the ultimate supremum of a stable Lévy process with no negative jumps

DOI10.1214/10-AOP598zbMath1235.60036arXiv1004.2133MaRDI QIDQ653307

Goran Peskir, Robert C. Dalang, Violetta Bernyk

Publication date: 9 January 2012

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.2133

zbMATH Keywords

optimal stoppingoptimal predictionfractional derivativecurved boundaryweakly singular Volterra integral equationfractional free-boundary problempolar kernelstable Lévy process with no negative jumpsstochastic process reflected at its supremum

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Fractional derivatives and integrals (26A33) Stopping times; optimal stopping problems; gambling theory (60G40) Prediction theory (aspects of stochastic processes) (60G25) Integro-differential operators (47G20)

Related Items (16)

Predicting the Supremum: Optimality of ‘Stop at Once or Not at All’ ⋮ Reflected spectrally negative stable processes and their governing equations ⋮ Geometrically Convergent Simulation of the Extrema of Lévy Processes ⋮ Predicting the last zero before an exponential time of a spectrally negative Lévy process ⋮ Existence of density functions for the running maximum of a Lévy-Itô diffusion ⋮ Intertwining certain fractional derivatives ⋮ Optimal detection of a hidden target: the median rule ⋮ Three-dimensional Brownian motion and the golden ratio rule ⋮ Quickest detection of a hidden target and extremal surfaces ⋮ Censored stable subordinators and fractional derivatives ⋮ The law of the supremum of a stable Lévy process with no negative jumps ⋮ Predicting the time at which a Lévy process attains its ultimate supremum ⋮ Spectral decomposition of fractional operators and a reflected stable semigroup ⋮ Exact simulation of the extrema of stable processes ⋮ Stochastic classical solutions for space-time fractional evolution equations on a bounded domain ⋮ Optimally Stopping at a Given Distance from the Ultimate Supremum of a Spectrally Negative Lévy Process

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