We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows us to recover previously known results about lookback options. In particular, our methodology induces a new proof of the optimality of Azéma-Yor solution of the SEP for a certain class of lookback options. Unlike the SEP technique, our approach applies to a large class of exotics and is suitable for numerical approximation techniques.

We investigate a matching game with transferable utility when some of the characteristics of the players are unobservable to the analyst. We allow for a wide class of distributions of unobserved heterogeneity, subject only to a separability assumption that generalizes Choo and Siow (2006). We first show that the stable matching maximizes a social gain function that trades off two terms. The first term is simply the average surplus due to the observable characteristics; and the second one can be interpreted as a generalized entropy function that reflects the impact of the unobserved characteristics. We use this result to derive simple closed-form formulae that identify the joint surplus in every possible match and the equilibrium utilities of all participants, given any known distribution of unobserved heterogeneity. Moreover, we show that if transfers are observed, then the pre-transfer utilities of both partners are also identified. We conclude by discussing some empirical approaches suggested by these results for the study of marriage markets, hedonic prices, and the market for CEOs.

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Abstract. We propose a computationally feasible way of deriving the identified set of parameter values in models with multiple equilibria, with particular emphasis on oligopoly entry models. This is achieved through an equivalence result between the existence of an equilibrium selection mechanism compatible with the observed data and a set of inequalities, and through an appeal to efficient linear programming techniques.