Generalized inverse Gaussian distributions and the time of first level crossing

2017/08/29 by V. K. Malinovskiǐ, Malinovskii, Vsevolod K. · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1708.08671

openalex publication_date 2017/08/29 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28

Abstract

We propose a new approximation for the distribution of the time of the first crossing of a high level u by random process \homVs-cs, where \homVs, s>0, is compound renewal process and c>0. It significantly outperforms the existing approximations, particularly in the region around the critical point c=\cS which separates processes with positive and negative drifts. This approximation is tightly related to generalized inverse Gaussian distributions.

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• On approximations for the distribution of the time of first level crossing

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