Approximating Perpetuities

Margarete Knape () and Ralph Neininger ()
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Margarete Knape: J.W. Goethe-University Frankfurt a.M.
Ralph Neininger: J.W. Goethe-University Frankfurt a.M.

Methodology and Computing in Applied Probability, 2008, vol. 10, issue 4, 507-529

Abstract: Abstract We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be approximated well.

Keywords: Perpetuity; Theory of distributions; Approximation of probability densities; Perfect simulation; Primary 60E99; Secondary 65C50, 65C10 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-007-9059-x

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