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

Key Points

• This research aims to derive explicit drawdown-based exit identities for Lévy processes observed at Poisson arrival times.
• Utilized fluctuation theory to analyze Lévy processes.
• Derived expressions for exit identities related to overshoots and undershoots.
• Expressed Laplace transforms of risk quantities using scale functions.
• Identified clear relationships between exit identities and Poisson observation times.
• Established new Laplace transforms for risk measures that involve drawdowns.
• Provided mathematical expressions applicable to spectrally negative Lévy processes.