A single formula assigns a continuous utility function to every representable preference relation.

Sufficient conditions are provided for a possibly incomplete preference preorder on a topological space to be closed in the product space if and only if it has closed upper and lower contour sets. Notably, it is shown that the two properties are equivalent if the domain of the preorder is a...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the...

This paper considers the robustness of optimal decisions in a model of monopoly and a model of competitive equilibrium in a securities market. Robustness, defined as payoffs being continuous with respect to perturbations in the underlying model, fails to hold for either model. Decision rules are...