Perpetual options and Canadization through fluctuation theory

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Chapter 2 Jump-Diffusion Models for Asset Pricing in Financial Engineering (2007, background): “See Asmussen et al. (2004), Boyarchenko and Levendorskĭı (2002), and Kyprianou and Pistorius (2003) for some representations (though not explicit calculations) based on the Wiener–Hopf factorization related to the overshoot problems for general Lévy processes; and see also Avram et al. (2004) and…”
On Threshold Strategies and the Smooth-Fit Principle for Optimal Stopping Problems (2007, background): “The second approach is based on fluctuation theory (see [16]) and relies on the computation of the Laplace transform of the hitting time at level x∗.”
On Exit and Ergodicity of the Spectrally One-Sided Lévy Process Reflected at Its Infimum (2004, background): “[1, 8, 20] and references therein.) Moreover, the reected L evy process occurs in relation with a problem associated with mathematical nance. See [ 17 ] and references therein.”
Option Pricing Under a Double Exponential Jump Diffusion Model (2004, background): “6 See, for example, Siegmund (1985), Boyarchenko and Levendorskiı̆ (2002b), and Kyprianou and Pistorius (2003) for some representations (though not explicit calculations) related to the overshoot problems for general Lévy processes.”