Fractional Poisson Process: Long-Range Dependence and Applications in Ruin Theory

2014/09/01 by Romain Biard, Bruno Saussereau · 69 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Actuarial science #Applied mathematics #Compound Poisson process #Computer science #Counting process #Distribution (mathematics) #Economics #Financial Risk and Volatility Modeling #Mathematical analysis #Mathematics #Poisson distribution #Poisson process #Probability and Risk Models #Process (computing) #Property (philosophy) #Range (aeronautics) #Renewal theory #Risk model #Risk theory #Ruin theory #Statistical Distribution Estimation and Applications #Statistical physics #Statistics

paper · pdf · doi:10.1239/jap/1409932670

published in Journal of Applied Probability 51(3), 727-740 (Cambridge University Press)

openalex publication_date 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study a renewal risk model in which the surplus process of the insurance company is modelled by a compound fractional Poisson process. We establish the long-range dependence property of this nonstationary process. Some results for ruin probabilities are presented under various assumptions on the distribution of the claim sizes.

Cited by

• On the long-range dependence of fractional Poisson and negative binomial processes
• NeuroMemFPP: A recurrent neural approach for memory-aware parameter estimation in fractional Poisson process
• Asymptotic Correlation Structure of Discounted Incurred But Not Reported Claims under Fractional Poisson Arrival Process
• Superposition of time-changed Poisson processes and their hitting times
• Multivariate fractional Poisson processes and compound sums
• Bayesian Modeling for Nonstationary Spatial Point Process via Spatial Deformations. [europepmc]

Related

• Fractional Risk Process in Insurance
• Large deviations for fractional Poisson processes
• Generalized Fractional Risk Process
• A Fractional Generalization of the Poisson Processes and Some of its Properties
• On the long-range dependence of fractional Poisson and negative binomial processes