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In this paper, we consider continuous-time Markov chains with a finite statespace under nonlinear expectations. We define so-called Q-operators as anextension of Q-matrices or rate matrices to a nonlinear setup, where thenonlinearity is due to model uncertainty. The main result gives a fullcharacterization of convex Q-operators in terms of a positive maximumprinciple, a dual representation by means of Q-matrices, continuous-time Markovchains under convex expectations and nonlinear ordinary differential equations.This extends a classical characterization of generators of Markov chains to thecase of model uncertainty in the generator. We further derive a primal and dualrepresentation of the convex semigroup arising from a Markov chain under aconvex expectation via the Fenchel-Legendre transformation of its generator. Weillustrate the results with several numerical examples, where we compute pricebounds for European contingent claims under model uncertainty in terms of therate matrix.

Markov chains under nonlinear expectation