Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/201635
Authors: 
Denk, Robert
Kupper, Michael
Nendel, Max
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 610
Abstract: 
We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of infinitesimal generators (Aλ) λ∈Λ of linear Lévy processes which guarantees the existence of a nonlinear Lévy process such that the corresponding nonlinear Markovian convolution semigroup is a viscosity solution of the fully nonlinear PDE ∂tu=supλ∈ΛAλu. The results are illustrated with several examples.
Subjects: 
Lévy process
convex expectation space
Markovian convolution semigroup
fully nonlinear PDE
Nisio semigroup
JEL: 
G51
L25
H20
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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