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We investigate optimal trading strategies under uncertainty in a nonparametric no-arbitrage framework that is consistent with an arbitrary number of assets. We show that extreme aversion to uncertainty precludes trading, and that preference for uncertainty induces market participation. <br> In an empirical exercise using S&P 500 options, we find that magnitudes of optimal portfolio positions are small when uncertainty is high, whereas risk-based models usually predict the opposite. They also strongly co-move with trading volume. Differences in beliefs modelled through differences in agents' ambiguity priors lead to an equilibrium in which agents' ambiguity aversion is persistent over time.