Wednesday, April 18, 2018 - 15:00 in V3-201
A semigroup approach to nonlinear Lévy processes
A talk in the Bielefeld Stochastic Afternoon series by
Max Nendel from Bielefeld
| Abstract: |
Nonlinear expectations, as introduced by S. Peng, are closely related to monetary
risk measures. Nonlinear expectations naturally appear in the context of pricing under model
uncertainty, e.g. drift uncertainty (g-expectation) or volatility uncertainty (G-expectation). In
this talk, we demonstrate how Lévy processes under nonlinear expectations arise from solutions
to certain fully nonlinear PDEs, where the Knigthian uncertainty is in the Lévy triplet. This
is done using nonlinear semigroups and a nonlinear version of Kolmogorov’s extension theorem.
We provide a sufficient condition for families of Lévy tiplets that guarantees the solvability
of the related fully nonlinear partial integro-differential equation, and show that the solution
admits a representation by means of a nonlinear Lévy process.
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