On Nonlinear Expectations and Markov Chains under Model Uncertainty

Max Nendel
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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

Abstract: 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)
Pages: 29
Date: 2019-11-29
New Economics Papers: this item is included in nep-ore
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https://pub.uni-bielefeld.de/download/2939265/2939266 First Version, 2019 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:628

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