2013/06/19 by Jean-Fran ccois Renaud, Renaud, Jean-François · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Risk Management (q-fin.RM)
paper · doi:10.48550/arxiv.1306.4619
openalex publication_date 2013/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as soon as the wealth process falls into the red zone and is brought back to its regular level when the process recovers. The analysis is mainly focused on the time a refracted Lévy risk process spends in the red zone (analogous to the duration of the negative surplus). Building on results from Kyprianou and Loeffen (2010) and Loeffen et al. (2012), we identify the distribution of various functionals related to occupation times of refracted spectrally negative Lévy processes. For example, these results are used to compute the probability of bankruptcy and the probability of Parisian ruin in this model with restructuring.