Nonlinear Lévy Processes and their Characteristics

Abstract

We develop a general construction for nonlinear Lévy processes with given characteristics. More precisely, given a set $\Theta$ 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 $\Theta$. 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.

36 pages; forthcoming in 'Transactions of the American Mathematical Society'

References in corpus (2)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Tightness, weak compactness of nonlinear expectations and application to CLT

Cited by in corpus (3)

• Measurability of Semimartingale Characteristics with Respect to the Probability Law
• On the properites of Poisson random measures associated with a G-Levy process
• Backward SDE Representation for Stochastic Control Problems with Non Dominated Controlled Intensity