A difference method for the McKean–Vlasov equation

We analyze a model equation arising in option pricing. This model equation takes the form of a nonlinear, nonlocal diffusion equation. We prove the well posedness of the Cauchy problem for this equation. Furthermore, we introduce a semidiscrete difference scheme and show its rate of convergence.

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2019-10, Vol.70 (5), p.1-24, Article 149
Main Authors: Coclite, Giuseppe Maria, Risebro, Nils Henrik
Format: Article
Language:English
Subjects:
Cauchy problems
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Vlasov equations
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Description
Summary:We analyze a model equation arising in option pricing. This model equation takes the form of a nonlinear, nonlocal diffusion equation. We prove the well posedness of the Cauchy problem for this equation. Furthermore, we introduce a semidiscrete difference scheme and show its rate of convergence.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-019-1196-x