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Exit identities for Lévy processes observed at Poisson arrival times. (English) Zbl 1338.60125
Summary: For a spectrally one-sided Lévy process, we extend various two-sided exit identities to the situation when the process is only observed at arrival epochs of an independent Poisson process. In addition, we consider exit problems of this type for processes reflected either from above or from below. The resulting Laplace transforms of the main quantities of interest are in terms of scale functions and turn out to be simple analogues of the classical formulas.

MSC:
60G51 Processes with independent increments; Lévy processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
91B30 Risk theory, insurance (MSC2010)
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