On Nonlinear Expectations and Markov Chains under Model Uncertainty
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Max Nendel: Center for Mathematical Economics, Bielefeld University
No 628, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University
The aim of this work is to give an overview on nonlinear expectation and to relate them to other concepts that describe model uncertainty or imprecision in a probabilistic framework. We discuss imprecise versions of stochastic processes with a particular interest in imprecise Markov chains. First, we focus on basic properties and representations of nonlinear expectations with additional structural assumptions such as translation invariance or convexity. In a second step, we discuss how stochastic processes under nonlinear expectations can be constructed via primal and dual representations. We illustrate the concepts by means of imprecise Markov chains with a countable state space, and show how families of Markov chains give rise to imprecise versions of Markov chains. We discuss dual representations and differential equations related to the latter.
Keywords: Nonlinear expectation; imprecise probability; Choquet capacity; imprecise Markov chain; nonlinear transition probability (search for similar items in EconPapers)
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:628
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