Consider a financial market in which an agent trades with utility-induced restrictions on wealth. For a utility function which satisfies the condition of reasonable asymptotic elasticity at −∞ we prove that the utility-based super-replication price of an unbounded (but sufficiently integrable) contingent claim is equal to the supremum of its discounted expectations under pricing measures with f...

An orbitope is the convex hull of an orbit of a point under the action of a compact group. We derive bounds on volumes of sections of polar bodies of orbitopes, extending methods developed in [BB03]. As an application we realize the cone of convex forms as a section of the cone of nonnegative bi-homogeneous forms and estimate its volume. A convex form has to be nonnegative, but it has not been ...

For a proper cone K ⊂ Rn and its dual cone K∗ the complementary slackness condition xT s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K∗ }. When K is a symmetric cone, this fact translates to a set of n linearly independent bilinear identities (optimality conditions) satisfied by every (x, s) ∈ C(K). This proves to be very useful when optimizing over such cones,...

Let S = {x ∈ Rn | f1(x) ≥ 0, . . . , fs(x) ≥ 0} be a basic closed semi-algebraic set in Rn and let PO(f1, . . . , fs) be the corresponding preordering in R[X1, . . . , Xn]. We examine for which polynomials f there exist identities f + εq ∈ PO(f1, . . . , fs) for all ε > 0. These are precisely the elements of the sequential closure of PO(f1, . . . , fs) with respect to the finest locally convex ...

Space tensors appear in physics and mechanics, and they are real physical entities. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In this short paper, we investigate these problems from the viewpoint o...

Elementary symmetric polynomials can be thought of as derivative polynomials of En(x) = ∏ i=1,...,n xi. Their associated hyperbolicity cones give a natural sequence of relaxations for R+. We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence ...

The system of isentropic Euler equations in the potential flow regime can be considered formally as a second order ordinary differential equation on the Wasserstein space of probability measures. This interpretation can be used to derive a variational time discretization. We prove that the approximate solutions generated by this discretization converge to a measure-valued solution of the isentr...

Consider a financial market in which an agent trades with utility-induced restrictions on wealth. We prove that the utility-based super-replication price of an unbounded (but sufficiently integrable) contingent claim is equal to the supremum of its discounted expectations under pricing measures with finite entropy. Central to our proof is the representation of a cone CV of utilitybased super-re...

The aim of this paper is to investigate partially ordered real linear topological spaces in which directed sets admit a supremum in their closure. In particular, we point out that this property is intimately related to the normality of the ordering cone and also to the Scott continuity of functionals belonging to the nonnegative polar of the ordering cone. Mathematics Subject Classification (20...

For a given element f ∈ L and a convex cone C ⊂ L, C∩ L + = {0} we give necessary and sufficient conditions for the existence of an element g ≥ f lying in the polar of C. This polar is taken in (L) and in L. In the context of mathematical finance the main result concerns the existence of martingale measures, whose densities are bounded from below by prescribed random variable.