Vector-valued weakly analytic measures

Vector - Valued Weakly Analytic

Vector-valued coherent risk measures

We define (d, n)−coherent risk measures as set-valued maps from Ld into IR satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from IR−valued random portfolio to IR−valued measure of risk. Necessary and sufficient conditions o...

Vector Valued Measures of Bounded Mean Oscillation

The duality between Hl and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained . Using the atomic decomposition approach ([C], [L]) the author studied the problem of characterizing the dual space of Hl of vector-valued functions . In [B2] the author showed, for the case SZ = {Iz1 = 1}, tha...

Characterizations of Vector-valued Weakly Almost Periodic Functions

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties. 1. Introduction. Let S be a semitopological semigroup, let ᐄ be...

Vector-valued Means and Weakly Almost Periodic Functions

Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T lZ2 (Received June 30, 1992 and in revised form November 7, 1992) ABSTRACT. A formula is set up between vector-vMued mean and scMax-valued that enbles translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-vMued means, .how tha...