We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. When these consumers trade in a sequence of markets, their time-inconsistency may introduce a non-convexity that gives them an incentive to trade lotteries. If there are many consumers, competitive equilibria with and without lotteries exist. The existence of symmetric equilibria may req...

Motivated by notions of aversion to Knightian uncertainty, this paper develops the theory of competitive asset pricing and consumption/portfolio choice with homothetic recursive preferences that allow essentially any homothetic uncertainty averse certainty-equivalent form. The market structure is scale invariant but otherwise general, allowing any trading constraints that scale with wealth. Tec...

For positive integers s and t, let f (sÒ t) denote the smallest positive integer N such that every 2-colouring of [1ÒN] = f1Ò 2Ò    ÒNg has a monochromatic homothetic copy of f1Ò 1 + sÒ 1 + s + tg. We show that f (sÒ t) = 4(s + t) + 1 whenever sÛg and tÛg are not congruent to 0 (modulo 4), where g = gcd(sÒ t). This can be viewed as a generalization of part of van der Waerden’s theorem on ari...

Abstract For all positive integers s and t, Brown et. al [1] defined f(s, t) to be the smallest positive integer N such that every 2-coloring of [1, N ] has a monochromatic homothetic copy of {1, 1+ s, 1+ s+ t}. They proved that f(s, t) ≤ 4(s + t) + 1 for all s, t and that the equality holds in the case where both s/g 6≡ 0 (mod 4) and t/g 6≡ 0 (mod 4) with g = gcd(s, t) and in many other cases....

We show how to use graphics hardware for tackling optimization problems arising in the field of computational geometry. We exemplarily discuss three problems, where combinatorial algorithms are inefficient or hard to implement. Given a set S of n point in the plane, the first two problems are to determine the smallest homothetic scaling of a star shaped polygon P enclosing S and to find the lar...

A novel method of texture primitive description using morphological skeleton is proposed. The skeleton of an object has the property that it is reduced to one point when the structuring element used for the skeletonization is exactly homothetic to the object. This method applies this property. This method minimizes the number of pixels contained in the skeleton. If we assume that the texture is...

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration ...