Expected utility of the drawdown-based regime-switching risk model with state-dependent termination

In this paper, we model an entity's surplus process X using the drawdown-based regime-switching (DBRS) dynamics proposed in Landriault et al. (2015a). We introduce the state-dependent termination time to the model, and provide rationale for its introduction in insurance contexts. By examining some related potential measures, we first derive an explicit expression for the expected terminal utility of the entity in the DBRS model with Brownian motion dynamics. The analysis is later generalized to time-homogeneous Markov framework, where the spectrally negative Lévy model is also discussed as a special example. Our results show that, even considering the impact of the termination risk, the DBRS strategy can still outperform its counterparts in either single regime strategy. This study shows that the DBRS model is not myopic, as it not only helps to recover from significant losses, but also may improve the insurer's overall welfare.