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

Authors:	Marjorie G Hahn Michael J Klass

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 is an independent Poisson random variable with parameter . 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 and Z and not on the overall exceedance level a.

Keywords:	Compound Poisson process Esscher transform approximation of exceedance levels
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