Analysis of a drawdown-based regime-switching Lévy insurance model

In this paper, we propose a new drawdown-based regime-switching (DBRS) Lévy insurance model in which the underlying drawdown process is used to model an insurer’s level of financial distress over time, and to trigger regime-switching transitions. By some analytical arguments, we derive explicit formulas for a generalized two-sided exit problem. We specifically state conditions under which the survival probability is not trivially zero (which corresponds to the positive security loading conditions of the proposed model). The regime-dependent occupation time until ruin is later studied. As a special case of the general DBRS model, a regime-switching premium model is given further consideration. Connections with other existing risk models (such as the loss-carry-forward tax model of Albrecher and Hipp, 2007) are established.