Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/233753
Authors: 
Nendel, Max
Year of Publication: 
2020
Citation: 
[Journal:] Mathematical Finance [ISSN:] 1467-9965 [Volume:] 31 [Issue:] 1 [Pages:] 474-507
Abstract: 
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.
Subjects: 
generator of nonlinear semigroup
imprecise Markov chain
model uncertainty
nonlinear expectation
nonlinear ODE
Persistent Identifier of the first edition: 
Creative Commons License: 
http://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
Document Version: 
Published Version

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