An equivalent sigma-martingale measure (EsigmaMM) for a given stochastic process S is a probability measure R equivalent to the original measure P such that S is an R-sigma-martingale. Existence of an EsigmaMM is equivalent to a classical absence-of-arbitrage property of S, and is invariant if...

Revealed preference restrictions are increasingly used to bound demand responses and as shape restrictions in nonparametric estimation exercises. However, the restrictions imposed are not sufficient for rationality when predictions are made at more than a single price regime. We highlight the...

This is a preliminary draft of the manuscript of my textbook "Optimal Transport Methods in Economics" (to appear), based on lectures given at MIT in Spring 2015. The present preprint version is circulated to invite comments by readers

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models. Often, it is known beforehand, that the underlying unknown function has certain properties, e.g., nonnegative or increasing on a certain region....

Consider two continuous functions f,g mapping the interval [0,S] of the real line into R. Let f also be strictly increasing. We are interested in the set of probability distributions on the interval [0,S] that maximize the expectation of f subject to the constraint that the expectation of g be...

With greater penetration of renewable generation, the uncertainty faced in electricity markets has increased substantially. Conventionally, generators are assigned a pre-dispatch quantity in advance of real time, based on estimates of uncertain quantities. Expensive real time adjustments then...

The main contents of this paper is two-fold. First, we present a method to approximate multivariate convex functions by piecewise linear upper and lower bounds. We consider a method that is based on function evaluations only. However, to use this method, the data have to be convex....

Revealed Preference offers nonparametric tests for whether consumption observations can be rationalized by a utility function. If a consumer is inconsistent with GARP, we might need a measure for the severity of inconsistency. One widely used measure is the Afriat efficiency index (AEI). We...