Geometrically Convergent Simulation of the Extrema of L\'{e}vy Processes

Jorge Ignacio Gonz\'alez C\'azares, Aleksandar Mijatovi\'c and Ger\'onimo Uribe Bravo

Papers from arXiv.org

Abstract: We develop a novel approximate simulation algorithm for the joint law of the position, the running supremum and the time of the supremum of a general L\'evy process at an arbitrary finite time. We identify the law of the error in simple terms. We prove that the error decays geometrically in $L^p$ (for any $p\geq 1$) as a function of the computational cost, in contrast with the polynomial decay for the approximations available in the literature. We establish a central limit theorem and construct non-asymptotic and asymptotic confidence intervals for the corresponding Monte Carlo estimator. We prove that the multilevel Monte Carlo estimator has optimal computational complexity (i.e. of order $\epsilon^{-2}$ if the mean squared error is at most $\epsilon^2$) for locally Lipschitz and barrier-type functionals of the triplet and develop an unbiased version of the estimator. We illustrate the performance of the algorithm with numerical examples.

Date: 2018-10, Revised 2021-06
New Economics Papers: this item is included in nep-cmp
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Mathematics of Operations Research 47(2) (2022) 1141-1168

Downloads: (external link)
http://arxiv.org/pdf/1810.11039 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1810.11039

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().