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Laplace transforms of the Brownian motion’s first exit from a strip. (English) Zbl 1488.60194

The author investigates the first exit time of a Brownian motion from a strip. Laplace transform is presented of the exit time. The strip boundaries are assumed to be continuous piecewise linear functions and the existence of deterministic terminal moment is supposed. Both cases – when the exit happens before and after the terminal date – are considered. The results obtained in the paper can be implemented in various numerical methods and algorithms.

MSC:

60J65 Brownian motion
44A10 Laplace transform
60G40 Stopping times; optimal stopping problems; gambling theory
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