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Nonlinear Lévy Processes and their Characteristics

We develop a general construction for nonlinear Lévy processes with given characteristics. More precisely, given a set $Θ$ of Lévy triplets, we construct a sublinear expectation on Skorohod space under which the canonical process has stationary independent increments and a nonlinear generator corresponding to the supremum of all generators of classical Lévy processes with triplets in $Θ$. The nonlinear Lévy process yields a tractable model for Knightian uncertainty about the distribution of jumps for which expectations of Markovian functionals can be calculated by means of a partial integro-differential equation.