Parisian ruin with power-asymmetric variance near the optimal point with application to many-inputs proportional reinsurance

Authors: Pavel Ievlev

Published in: Stochastic Models (2023)

Date: January 2023

doi arxiv

Abstract

This paper investigates the Parisian ruin probability for processes with power-asymmetric behavior of the variance near the unique optimal point. We derive the exact asymptotics as the ruin boundary tends to infinity and extend the previous result arXiv:1504.07061 to the case when the length of Parisian interval is of Pickands scale. As a primary application, we extend the recent result arXiv:2010.00222 on the many inputs proportional reinsurance fractional Brownian motion risk model to the Parisian ruin.

Keywords

Parisian ruin, Ruin probability, fractional Brownian motion

BibTeX

@article {MR4777226,
    AUTHOR = {Ievlev, Pavel},
    TITLE = {Parisian ruin with power-asymmetric variance near the optimal              point with application to many-inputs proportional reinsurance},
    JOURNAL = {Stoch. Models},
    FJOURNAL = {Stochastic Models},
    VOLUME = {40},
    YEAR = {2024},
    NUMBER = {3},
    PAGES = {518--535},
    ISSN = {1532-6349,1532-4214},
    MRCLASS = {60G15 (60G70)},
    MRNUMBER = {4777226},
    DOI = {10.1080/15326349.2023.2278527},
    URL = {https://doi.org/10.1080/15326349.2023.2278527}
}