Optimal Portfolio Positioning on Multiple Assets Under Ambiguity

Abstract

This paper determines the optimal financial portfolio in the multidimensional setting when the investor exhibits ambiguity aversion. We consider the Maccheroni et al. (Econometrica 74(6):1447–1498, 2006) framework which includes both the Gilboa and Schmeidler’s (J Math Econ 18(2):141–153, 1989) multiple priors preferences and the (American Econ Rev 91:60–66, 2001) multiplier preferences. We determine the optimal portfolio profile under ambiguity when the investors can invest on various risky assets. We investigate in particular the CRRA case while introducing an ambiguity index based on the relative entropy criterion. Such result extends Ben Ameur and Prigent (Econ Model 34:89–97, 2013) when there is only one risky asset. Indeed, we show for example how the ambiguity on the correlations between the risky assets crucially modify the optimal payoff. Such results have important practical applications in structured portfolio management when investing on multiple financial indices and basket options.