General drawdown-based exit identities for Lévy processes observed at poisson arrival time

This paper derives explicit expressions for drawdown-based two-sided exit identities involving the overshoots and undershoots at the exit times under Poisson observation times for spectrally negative Lévy risk processes by using fluctuation theory. All resulting Laplace transforms of the risk quantities of interest are expressed in terms of the scale functions of the spectrally negative Lévy processes.