Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs | Zendy

Denis Belomestny | Zendy; Tigran Nagapetyan | Zendy

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Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs

Author(s) -

Denis Belomestny,

Tigran Nagapetyan

Publication year - 2017

Publication title -

bernoulli

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.814

H-Index - 72

eISSN - 1573-9759

pISSN - 1350-7265

DOI - 10.3150/15-bej764

Subject(s) - mathematics , discretization , stochastic differential equation , weak convergence , convergence (economics) , monte carlo method , simple (philosophy) , euler method , path (computing) , coupling (piping) , euler's formula , backward euler method , mathematical optimization , statistical physics , mathematical analysis , computer science , physics , mechanical engineering , philosophy , statistics , computer security , epistemology , engineering , economics , asset (computer security) , programming language , economic growth

In this paper, we discuss the possibility of using multilevel Monte Carlo (MLMC) approach for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler schemes for Lévy-driven stochastic differential equations. The numerical performance of the new "weak" MLMC method is illustrated by several numerical examples

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