TY  - JOUR
AB  - In this paper, we consider continuous-time Markov chains with a finite state space under nonlinear expectations. We define so-called Q-operators as an extension of Q-matrices or rate matrices to a nonlinear setup, where the nonlinearity is due to model uncertainty. The main result gives a full characterization of convex Q-operators in terms of a positive maximum principle, a dual representation by means of Q-matrices, time-homogeneous Markov chains under convex expectations, and a class of nonlinear ordinary differential equations. This extends a classical characterization of generators of Markov chains to the case of model uncertainty in the generator. We further derive an explicit primal and dual representation of convex semigroups arising from Markov chains under convex expectations via the Fenchel-Legendre transformation of the generator. We illustrate the results with several numerical examples, where we compute price bounds for European contingent claims under model uncertainty in terms of the rate matrix.
DA  - 2021
DO  - 10.1111/mafi.12289
KW  - generator of nonlinear semigroup
KW  - imprecise Markov chain
KW  - model
KW  - uncertainty
KW  - nonlinear expectation
KW  - nonlinear ODE
LA  - eng
IS  - 1
M2  - 474
PY  - 2021
SN  - 0960-1627
SP  - 474-507
T2  - Mathematical Finance
TI  - Markov chains under nonlinear expectation
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29489276
Y2  - 2024-11-21T22:49:50
ER  -