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Exact simulation of generalised Vervaat perpetuities

Dassios, Angelos, Lim, Jia Wei and Qu, Yan (2019) Exact simulation of generalised Vervaat perpetuities. Journal of Applied Probability. ISSN 0021-9002 (In Press)

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Abstract

We consider a generalised Vervaat perpetuity of the form X = Y1W1 + Y2W1W2 + ..., where Wi ~ U1/t and (Yi)i≥0 is an i.i.d sequence of random variables independent from (Wi)i≥0. Based on a distributional decomposition technique, we propose a novel method for exactly simulating the generalised Vervaat perpetuity. The general framework relies on the exact simulation of the truncated Gamma process, which we develop using a marked renewal representation for its paths. Furthermore, a special case arises when Yi = 1, and X has the generalised Dickman distribution, for which we present an exact simulation algorithm using the marked renewal approach. In particular, this new algorithm is much faster than existing algorithms illustrated in Devroye and Fawzi (2010), Fill and Huber (2010), Chi (2012), and Cloud and Huber (2017) as well as being applicable to the general payments case. Examples and numerical analysis are provided to demonstrate the accuracy and effectiveness of our method.

Item Type: Article
Official URL: https://www.cambridge.org/core/journals/journal-of...
Additional Information: © 2019 Cambridge University Press
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 03 Jan 2019 15:56
Last Modified: 31 Jan 2019 17:48
URI: http://eprints.lse.ac.uk/id/eprint/91489

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