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Least Squares Estimator for Path-Dependent McKean-Vlasov SDEs via Discrete-Time Observations
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...
Published in: | Acta Mathematica Scientia |
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ISSN: | 0252-9602 1572-9087 |
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Springer Science and Business Media LLC
2019
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URI: | https://cronfa.swan.ac.uk/Record/cronfa44860 |
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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 0000-0003-4568-7013 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 0000-0003-4568-7013 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 |
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|
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facultyofscienceandengineering |
hierarchy_top_title |
Faculty of Science and Engineering |
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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 |
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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 |
2019-05-01T03:56:19Z |
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1763752835203203072 |
score |
11.021648 |