Risk modelling on liquidations with Lévy processes

Abstract

In classical ruin theory, the time of ruin is defined as the time when the surplus of an insurance portfolio falls below zero. This simplification of a single barrier, however, needs careful adaptations to imitate the real-world liquidation process. Inspired by [7] and [24], this paper adopts a three-barrier model to describe the financial stress leading to bankruptcy of an insurer. The financial status of the insurer is classified into three states, namely, the solvent, the insolvent, and the liquidated. The insurer's surplus processes at the states of solvent and insolvent are modeled by two spectrally negative Lévy processes, which have been taken as good candidates to model insurance ris..