2022/06/19 by Shota Nakamura, Nakamura, Shota, Yasutaka Shimizu +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #60G22 #60H07 #62P05 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Statistics Theory (math.ST) #math.PR #math.ST #msc:60G22 #msc:60H07 #msc:62P05 #stat.TH
paper · pdf · doi:10.48550/arxiv.2206.09441
arxiv created 2022/06/19 · openalex publication_date 2022/06/19 · arxiv updated 2022/06/22 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28
We consider a surplus process of drifted fractional Brownian motion with the Hurst index H>1/2, which appears as a functional limit of drifted compound Poisson risk models with correlated claims, and this is a kind of representation of a surplus with a long memory. Our interest is to construct confidence intervals of the ruin probability of the surplus when the volatility parameter is unknown. We will obtain the derivative of the ruin probability w.r.t. the volatility parameter via Malliavin calculus, and apply the delta method to identify the asymptotic distribution of an estimated ruin probability.