Large deviations for fractional Poisson processes

2012/04/06 by Luisa Beghin, Beghin, Luisa, Claudio Macci +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #33E12 #60F10 #60G22 #60K05 #91B30 #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models

paper · pdf · doi:10.48550/arxiv.1204.1446

openalex publication_date 2012/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance model with constant premium rate, i.i.d. light tail claim sizes, and a fractional Poisson claim number process. We conclude with the alternative version where all the random variables are weighted Poisson distributed. Keywords: Mittag Leffler function; renewal process; random time cha

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