Rare event simulation for processes generated via stochastic fixed point equations

DOI10.1214/13-AAP974zbMath1316.65015arXiv1107.3284MaRDI QIDQ744388

Guoqing Diao, Jeffrey F. Collamore, Anand N. Vidyashankar

Publication date: 25 September 2014

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

Full work available at URL: https://arxiv.org/abs/1107.3284

zbMATH Keywords

importance samplinglarge deviationMonte Carlo methodsfinancial time seriesrisk theoryregeneration timesARCH processeslast exit timesnonlinear renewal theoryfirst entrance timesHarris recurrent Markov chainsruin theory with stochastic invesments

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Economic time series analysis (91B84) Discrete-time Markov processes on general state spaces (60J05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Numerical analysis or methods applied to Markov chains (65C40) Random operators and equations (aspects of stochastic analysis) (60H25) Stopping times; optimal stopping problems; gambling theory (60G40) Large deviations (60F10) Markov renewal processes, semi-Markov processes (60K15)

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Importance sampling approximations to various probabilities of ruin of spectrally negative Lévy risk processes ⋮ Importance sampling for maxima on trees ⋮ Large excursions and conditioned laws for recursive sequences generated by random matrices ⋮ On the Kesten–Goldie constant ⋮ Efficient rare-event simulation for perpetuities ⋮ Tail estimates for stochastic fixed point equations via nonlinear renewal theory ⋮ Importance sampling of heavy-tailed iterated random functions ⋮ Limit theory and robust evaluation methods for the extremal properties of GARCH\((p,q)\) processes

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