L  2-convergence rate for the discretization error of functions of Lévy process

Takafumi Amaba; Nien Lin Liu; Azmi Makhlouf; Takwa Saidaoui

doi:10.1080/17442508.2019.1642338

L ²-convergence rate for the discretization error of functions of Lévy process

Takafumi Amaba
, Nien Lin Liu
, Azmi Makhlouf
, Takwa Saidaoui

ビジネスエコノミクス学科

研究成果: Article › 査読

2 被引用数 (Scopus)

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In this article, we investigate the (Formula presented.) -convergence rate for the discretization error of the Clark-Ocone representation of a random variable (Formula presented.), where (Formula presented.) is a pure-jump Lévy process. As in the Brownian case, we find that the exact rate is subject to the Sobolev-differentiability index (in the sense of classical Malliavin calculus) of the space to which (Formula presented.) belongs.

本文言語	English
ページ（範囲）	566-594
ページ数	29
ジャーナル	Stochastics
巻	92
号	4
DOI	https://doi.org/10.1080/17442508.2019.1642338
出版ステータス	Published - 18 5月 2020

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@article{ffbeaf76828d4c9db1fa00677e2ca015,

title = " L 2-convergence rate for the discretization error of functions of L{\'e}vy process",

abstract = "In this article, we investigate the (Formula presented.) -convergence rate for the discretization error of the Clark-Ocone representation of a random variable (Formula presented.), where (Formula presented.) is a pure-jump L{\'e}vy process. As in the Brownian case, we find that the exact rate is subject to the Sobolev-differentiability index (in the sense of classical Malliavin calculus) of the space to which (Formula presented.) belongs.",

keywords = "Clark-Ocone formula, Discretization error of stochastic integral, Sobolev differentiability, discrete-time Clark-Ocone formula, hedging error",

author = "Takafumi Amaba and Liu, \{Nien Lin\} and Azmi Makhlouf and Takwa Saidaoui",

note = "Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2020",

month = may,

day = "18",

doi = "10.1080/17442508.2019.1642338",

language = "English",

volume = "92",

pages = "566--594",

journal = "Stochastics",

issn = "1744-2508",

publisher = "Gordon and Breach Science Publishers",

number = "4",

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TY - JOUR

T1 - L 2-convergence rate for the discretization error of functions of Lévy process

AU - Amaba, Takafumi

AU - Liu, Nien Lin

AU - Makhlouf, Azmi

AU - Saidaoui, Takwa

PY - 2020/5/18

Y1 - 2020/5/18

N2 - In this article, we investigate the (Formula presented.) -convergence rate for the discretization error of the Clark-Ocone representation of a random variable (Formula presented.), where (Formula presented.) is a pure-jump Lévy process. As in the Brownian case, we find that the exact rate is subject to the Sobolev-differentiability index (in the sense of classical Malliavin calculus) of the space to which (Formula presented.) belongs.

AB - In this article, we investigate the (Formula presented.) -convergence rate for the discretization error of the Clark-Ocone representation of a random variable (Formula presented.), where (Formula presented.) is a pure-jump Lévy process. As in the Brownian case, we find that the exact rate is subject to the Sobolev-differentiability index (in the sense of classical Malliavin calculus) of the space to which (Formula presented.) belongs.

KW - Clark-Ocone formula

KW - Discretization error of stochastic integral

KW - Sobolev differentiability

KW - discrete-time Clark-Ocone formula

KW - hedging error

UR - https://www.scopus.com/pages/publications/85087433896

U2 - 10.1080/17442508.2019.1642338

DO - 10.1080/17442508.2019.1642338

M3 - Article

AN - SCOPUS:85087433896

SN - 1744-2508

VL - 92

SP - 566

EP - 594

JO - Stochastics

JF - Stochastics

IS - 4

ER -

L 2-convergence rate for the discretization error of functions of Lévy process

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L ²-convergence rate for the discretization error of functions of Lévy process