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Numerical simulation of quadratic BSDEs
| hal.structure.identifier | Department of Mathematics [Imperial College London] | |
| dc.contributor.author | CHASSAGNEUX, Jean-François | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | RICHOU, Adrien | |
| dc.date.accessioned | 2024-04-04T03:20:30Z | |
| dc.date.available | 2024-04-04T03:20:30Z | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 1050-5164 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194590 | |
| dc.description.abstractEn | This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to $z$ and bounded terminal conditions. We first study a slight modification of the classical dynamic programming equation arising from the time-discretization of BSDEs. By using a linearization argument and BMO martingales tools, we obtain a comparison theorem, a priori estimates and stability results for the solution of this scheme. Then we provide a control on the time-discretization error of order $\frac{1}{2}-\varepsilon$ for all $\varepsilon>0$. In the last part, we give a fully implementable algorithm for quadratic BSDEs based on quantization and illustrate our convergence results with numerical examples. | |
| dc.description.sponsorship | Effets de Liquidité, contrôle des risques et EDSRs - ANR-11-JS01-0007 | |
| dc.language.iso | en | |
| dc.publisher | Institute of Mathematical Statistics (IMS) | |
| dc.title.en | Numerical simulation of quadratic BSDEs | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1214/14-AAP1090 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1307.5741 | |
| bordeaux.journal | The Annals of Applied Probability | |
| bordeaux.volume | 26 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00990555 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00990555v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=The%20Annals%20of%20Applied%20Probability&rft.date=2016&rft.volume=26&rft.issue=1&rft.eissn=1050-5164&rft.issn=1050-5164&rft.au=CHASSAGNEUX,%20Jean-Fran%C3%A7ois&RICHOU,%20Adrien&rft.genre=article |
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