Optimal Upper and Lower Bounds for the Upper Tails of Compound Poisson Processes

Marjorie G. Hahn and Michael J. Klass

Journal of Theoretical Probability, 1998, vol. 11, issue 2, 535-559

Abstract: Abstract A compound Poisson process is of the form $$S_{N_\lambda } = \sum\nolimits_{j = 1}^{N_\lambda } {Z_j }$$ where Z, Z 1, Z 2, are arbitrary i.i.d. random variables and N λ is an independent Poisson random variable with parameter λ. This paper identifies the degree of precision that can be achieved when using exponential bounds together with a single truncation to approximate $$P(S_{N_\lambda } \geqslant \lambda a)$$ . The truncation level introduced depends only on λ and Z and not on the overall exceedance level λa.

Keywords: Compound Poisson process; Esscher transform; approximation of exceedance levels (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022696125272

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