Non-linear affine processes with jumps

Abstract

We present a probabilistic construction of -valued non-linear affine processes with jumps. Given a set of affine parameters, we define a family of sublinear expectations on the Skorokhod space under which the canonical process X is a (sublinear) Markov process with a non-linear generator. This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation.