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

2014/09/01 by Romain Biard, Bruno Saussereau · 5 citations
Decision Sciences · Mathematics · Economics, Econometrics and Finance · #Probability and Risk Models #Statistical Distribution Estimation and Applications #Financial Risk and Volatility Modeling

paper · pdf · doi:10.1239/jap/1409932670

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.

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