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Exact simulation of extrinsic stress-release processes

Published online by Cambridge University Press:  14 February 2022

Young Lee*
Harvard University
Patrick J. Laub*
University of New South Wales
Thomas Taimre*
University of Queensland
Hongbiao Zhao*
Shanghai University of Finance and Economics
Jiancang Zhuang*
Institute of Statistical Mathematics
*Postal address: Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA. Email
**Postal address: School of Risk and Actuarial Studies, UNSW Business School, UNSW Sydney, Sydney, NSW 2052, Australia. Email address:
***Postal address: School of Mathematics and Physics, The University of Queensland, St Lucia, QLD 4072, Australia. Email address:
****Postal address: Shanghai University of Finance and Economics, Yangpu District, Shanghai, 200433, China. Email address:
*****Postal address: The Institute of Statistical Mathematics, 10-3 Midori-Cho, Tachikawa-Shi, Tokyo 190-8562, Japan. Email address:


We present a new and straightforward algorithm that simulates exact sample paths for a generalized stress-release process. The computation of the exact law of the joint inter-arrival times is detailed and used to derive this algorithm. Furthermore, the martingale generator of the process is derived, and induces theoretical moments which generalize some results of [3] and are used to demonstrate the validity of our simulation algorithm.

Original Article
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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