Optimal portfolio with vector expected utility

We study the optimal portfolio selected by an investor who conforms to Siniscalchi (2009)'s Vector Expected Utility's (VEU) axioms and who is ambiguity averse. To this end, we derive a mean-variance preference generalised to ambiguity from the second-order Taylor-Young expansion of the VEU certainty equivalent. We apply this Mean-Variance Variability preference to the static two-assets portfolio problem and deduce asset allocation results which extend the mean-variance analysis to ambiguity in the VEU framework. Our criterion has attractive features: it is axiomatically well-founded and analytically tractable, it is therefore well suited for applications to asset pricing as proved by a novel analysis of the home-bias puzzle with two ambiguous assets.