Optimal Hedging of a Contingent Claim with Ambiguity Aversion

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We propose a model of hedging and investment with ambiguity aversion in an incomplete financial market. We show that the agent's worst-case belief depends upon the payoff of the derivative to be hedged. Thus, we identify situations where one can distinguish ambiguity averse agents from probabilistically sophisticated agents. Further, we generate the hypothesis: an ambiguity averse agent chooses higher volatility when hedging a derivative position whose payoff function is convex than when hedging a position whose payoff function is concave. Our model can be extended to accommodate non-iid uncertainty and jumps in the continuous time limit of the model.