Markov chains under nonlinear expectation

Nendel M (2021)
Mathematical Finance 31(1): 474-507.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
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.
Stichworte
generator of nonlinear semigroup; imprecise Markov chain; model; uncertainty; nonlinear expectation; nonlinear ODE
Erscheinungsjahr
2021
Zeitschriftentitel
Mathematical Finance
Band
31
Ausgabe
1
Seite(n)
474-507
ISSN
0960-1627
eISSN
1467-9965
Finanzierungs-Informationen
Open-Access-Publikationskosten wurden durch die Universität Bielefeld im Rahmen des DEAL-Vertrags gefördert.
Page URI
https://pub.uni-bielefeld.de/record/2948927

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Nendel M. Markov chains under nonlinear expectation. Mathematical Finance . 2021;31(1):474-507.
Nendel, M. (2021). Markov chains under nonlinear expectation. Mathematical Finance , 31(1), 474-507. doi:10.1111/mafi.12289
Nendel, M. (2021). Markov chains under nonlinear expectation. Mathematical Finance 31, 474-507.
Nendel, M., 2021. Markov chains under nonlinear expectation. Mathematical Finance , 31(1), p 474-507.
M. Nendel, “Markov chains under nonlinear expectation”, Mathematical Finance , vol. 31, 2021, pp. 474-507.
Nendel, M.: Markov chains under nonlinear expectation. Mathematical Finance . 31, 474-507 (2021).
Nendel, Max. “Markov chains under nonlinear expectation”. Mathematical Finance 31.1 (2021): 474-507.
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2021-02-05T12:29:09Z
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