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Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations

Panpan Ren, Jiang-lun Wu

Acta Mathematica Scientia, Volume: 39, Issue: 3, Pages: 691 - 716

Swansea University Authors: Panpan Ren, Jiang-lun Wu

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DOI (Published version): 10.1007/s10473-019-0305-4

Abstract

In this paper, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establish...

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Published in: Acta Mathematica Scientia
ISSN: 0252-9602 1572-9087
Published: Springer Science and Business Media LLC 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa44860
first_indexed 2018-10-11T13:29:05Z
last_indexed 2023-01-11T14:21:40Z
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spelling 2022-08-21T21:32:24.4229737 v2 44860 2018-10-11 Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations 730d4aa09026fef7d3d03653815692aa Panpan Ren Panpan Ren true false dbd67e30d59b0f32592b15b5705af885 Jiang-lun Wu Jiang-lun Wu true false 2018-10-11 In this paper, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of our paper lie in three aspects: (i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works; (ii) We take the advantage of linear interpolation with respect to the discrete-timeobservations to approximate the functional solution; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (e.g., H\"older continuous) and path-distribution dependent. Journal Article Acta Mathematica Scientia 39 3 691 716 Springer Science and Business Media LLC 0252-9602 1572-9087 McKean-Vlasov stochastic differential equation, tamed Euler-Maruyama scheme, weak monotonicity, least squares estimator, consistency, asymptotic distribution. 1 5 2019 2019-05-01 10.1007/s10473-019-0305-4 http://dx.doi.org/10.1007/s10473-019-0305-4 COLLEGE NANME COLLEGE CODE Swansea University Other None 2022-08-21T21:32:24.4229737 2018-10-11T12:54:31.3521944 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Panpan Ren 1 Jiang-lun Wu 2 0044860-11102018130113.pdf correctV-distributionSDE(Tamed).pdf 2018-10-11T13:01:13.4670000 Output 322377 application/pdf Accepted Manuscript true 2020-05-07T00:00:00.0000000 Released under the terms of a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND). true eng
title Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
spellingShingle Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
Panpan Ren
Jiang-lun Wu
title_short Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
title_full Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
title_fullStr Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
title_full_unstemmed Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
title_sort Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
author_id_str_mv 730d4aa09026fef7d3d03653815692aa
dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv 730d4aa09026fef7d3d03653815692aa_***_Panpan Ren
dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Panpan Ren
Jiang-lun Wu
author2 Panpan Ren
Jiang-lun Wu
format Journal article
container_title Acta Mathematica Scientia
container_volume 39
container_issue 3
container_start_page 691
publishDate 2019
institution Swansea University
issn 0252-9602
1572-9087
doi_str_mv 10.1007/s10473-019-0305-4
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1007/s10473-019-0305-4
document_store_str 1
active_str 0
description In this paper, we are interested in least squares estimator for a class of path-dependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of our paper lie in three aspects: (i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works; (ii) We take the advantage of linear interpolation with respect to the discrete-timeobservations to approximate the functional solution; (iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (e.g., H\"older continuous) and path-distribution dependent.
published_date 2019-05-01T19:34:18Z
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score 11.04748

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