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Markov Chains under Nonlinear Expectation

Author

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  • Nendel, Max

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper, we consider nonlinear continuous-time Markov chains with a finite state space. We define so-called *Q*-operators as an extension of *Q*-matrices to a nonlinear setup, where the nonlinearity is due to parameter 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, continuous-time Markov chains under convex expectations and fully nonlinear ODEs. This extends a well-known characterization of *Q*-matrices.

Suggested Citation

  • Nendel, Max, 2018. "Markov Chains under Nonlinear Expectation," Center for Mathematical Economics Working Papers 588, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:588
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    File URL: https://pub.uni-bielefeld.de/download/2930411/2930412
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    References listed on IDEAS

    as
    1. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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