We consider two random vectors X and Y, such that the components of X are dominated in the convex order by the corresponding components of Y. We want to find conditions under which this implies that any positive linear combination of the components of X is dominated in the convex order by the...

We consider the optimization problem of a decision maker facing a sequence of coin tosses with an initially unknown probability Θ for heads. Before each toss she bets on either heads or tails and she wins one euro if she guesses correctly, otherwise she loses one euro. We investigate the effect...

There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity....

Consider a choice between two random variables, for which only means and variances are known. Is it possible to rank them by putting some constraints on risk preferences? We provide such a ranking by bounding how much marginal utility can change. Such bounds enable us to rank all distributions...