Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet-Brownian motions

Robert Kast (1) , André Lapied (2) , David Roubaud (3)

1 LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée
2 AMU - Aix Marseille Université
3 Montpellier Business School

Ambiguity is pervasive in many environments and is increasingly being introduced into economic and financial models. This paper characterises ambiguity in the form of newly defined Choquet random walks: discrete-time binomial trees with capacities instead of exact probabilities on their branches. We describe the axiomatic basis of Choquet random walks, including dynamic consistency. We also discuss the convergence of Choquet random walks to Choquet-Brownian motion in continuous time. In contrast to previous literature, we derive tractable stochastic processes that allow for a wide range of ambiguity preferences to be represented in continuous time (including ambiguity-seeking preferences). Finally, we apply Choquet-Brownian ambiguity to a model of stationary inter-temporal portfolio choice. We find that both the mean and the variance of the underlying stochastic process are modified. This result opens the way for qualitative and quantitative results that differ from those of standard expected utility models and other models that feature ambiguity.

Mots clés: Ambiguity models; Choquet-Brownian motion; Random walk; Dynamic consistency

Mots clés: Capacities

Domaines: Sciences de l'Homme et Société

Robert Kast, André Lapied, David Roubaud. Modelling under ambiguity with dynamically consistent Choquet random walks and Choquet-Brownian motions. Economic Modelling, 2014, 38 (C), pp.495-503. ⟨10.1016/j.econmod.2014.01.007⟩. ⟨hal-02633613⟩