A ruin model with a resampled environment

Constantinescu, C ORCID: 0000-0002-5219-3022, Delsing, G, Mandjes, M and Nandayapa, L Rojas (2020) A ruin model with a resampled environment SCANDINAVIAN ACTUARIAL JOURNAL, 2020 (4). pp. 323-341. ISSN 0346-1238, 1651-2030

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Abstract

This paper considers a Cramér–Lundberg risk setting, where the components of the underlying model change over time. We allow the more general setting of the cumulative claim process being modeled as a spectrally positive Lévy process. We provide an intuitively appealing mechanism to create such parameter uncertainty: at Poisson epochs, we resample the model components from a finite number of d settings. It results in a setup that is particularly suited to describe situations in which the risk reserve dynamics are affected by external processes. We extend the classical Cramér–Lundberg approximation (asymptotically characterizing the all-time ruin probability in a light-tailed setting) to this more general setup. In addition, for the situation that the driving Lévy processes are sums of Brownian motions and compound Poisson processes, we find an explicit uniform bound on the ruin probability. In passing we propose an importance-sampling algorithm facilitating efficient estimation, and prove it has bounded relative error. In a series of numerical experiments we assess the accuracy of the asymptotics and bounds, and illustrate that neglecting the resampling can lead to substantial underestimation of the risk.

Item Type:	Article
Uncontrolled Keywords:	Levy risk processes, parameter uncertainty, ruin probabilities, Cramer-Lundberg asymptotics, Lundberg's inequality
Depositing User:	Symplectic Admin
Date Deposited:	24 Jun 2019 14:53
Last Modified:	16 Jun 2026 14:01
DOI:	10.1080/03461238.2019.1667424
Open Access URL:	https://doi.org/10.1080/03461238.2019.1667424
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3046916
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