A high order weak approximation for jump-diffusions using Malliavin calculus and operator splitting

The paper introduces a novel high order discretization scheme for expectation of jump-diffusion processes by using a Malliavin calculus approach and an operator splitting method. The test function of the target expectation is assumed to be only Lipschitz continuous in order to apply the method to fi...

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Bibliographic Details
Published inMonte Carlo methods and applications Vol. 28; no. 2; pp. 97 - 110
Main Authors Akiyama, Naho, Yamada, Toshihiro
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.06.2022
Walter de Gruyter GmbH
Subjects
60H07
60H35
65C05
65C30
91G60
Algorithms
Discretization
jump-diffusion
Malliavin calculus
Mathematical analysis
operator splitting
Operators (mathematics)
Splitting
stochastic differential equation
Weak approximation
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Summary:The paper introduces a novel high order discretization scheme for expectation of jump-diffusion processes by using a Malliavin calculus approach and an operator splitting method. The test function of the target expectation is assumed to be only Lipschitz continuous in order to apply the method to financial problems. Then Kusuoka’s estimate is employed to justify the proposed discretization scheme. The algorithm with a numerical example is shown for implementation.
ISSN:0929-9629
1569-3961
DOI:10.1515/mcma-2022-2109