First Exit Times for Ordinary and Compound Poisson Processes with Non-linear Boundaries

S. Zacks ()
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S. Zacks: Binghamton University

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 3, 359-375

Abstract: Abstract Distributions of the first-exit times from a region with concave upper boundary are discussed for ordinary and compound Poisson processes. Explicit formulae are developed for the case of ordinary Poisson processes. Recursive formulae are given for the compound Poisson case, where the jumps are positive, having discrete or continuous distributions with finite means. Applications to sequential point estimation and insurance are illustrated.

Keywords: Stopping times; Sequential estimation; Non-linear boundaries; Compound Poisson processes; 60G51; 60K15; 60K40 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s11009-007-9024-8

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