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David Roubaud, Alain Lapied and Robert Kast
''Modelling under ambiguity with two correlated Choquet-Brownian motions''
( 2017, Vol. 37 No.2 )
Modelling under ambiguity in financial and economic models implies a sound characterisation of ambiguity sources. We expand the seminal work of Kast et al. (2014) who first defined Choquet Random Walks (CRW) and Choquet-Brownian Motions (CBM). Their work allows modelling in the presence of a single source of ambiguity and is used in various contexts, such as investment decisions and portfolio choices. As it is often useful (or even imperative) to introduce multiple sources of ambiguity, we expand the Choquet Brownian model for two correlated sources of ambiguity. Using properties of correlation, we first establish key results for correlated dynamically coherent Choquet Random Walks. We extend it to continuous-time for two correlated sources of ambiguity, each represented by a Choquet-Brownian Motion. Thus, we demonstrate that CBM are sufficiently tractable to adapt to more complex model settings, in the presence of uncertainty represented through two correlated sources of ambiguity. We apply our theoretical model to the optimal portfolio choice of traded assets.
Keywords: Ambiguity models; Choquet-Brownian Motion; correlated random walk Ambiguity models, Choquet-Brownian Motion, correlated random walk
JEL: D8 - Information, Knowledge, and Uncertainty: General
D9 - Intertemporal Choice and Growth: General
Manuscript Received : Apr 11 2017 Manuscript Accepted : May 05 2017

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