Titelaufnahme

Titel
On nonlinear expectations and Markov chains under model uncertainty / Max Nendel
VerfasserNendel, Max
ErschienenBielefeld, Germany : Center for Mathematical Economics (IMW), Bielefeld University, November 2019
Ausgabe
Elektronische Ressource
Umfang1 Online-Ressource (28 Seiten)
SerieCenter for Mathematical Economics Working papers ; 628
URNurn:nbn:de:hbz:6:2-129730 
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 Das Werk ist frei verfügbar
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On nonlinear expectations and Markov chains under model uncertainty [0.46 mb]
Zusammenfassung

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.

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