Vector-valued probability measures on semigroups

Interval-Valued Probability Measures

The purpose of this paper is propose a simple de…nition of an interval-valued probability measure and to examine some of the implications of this de…nition. This de…nition provides a method for characterizing certain types of imprecise probabilities. We develop some properties of this de…nition and propose a de…nition of integration with respect to it. We show that this de…nition is a generaliz...

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...

Hyperreal-Valued Probability Measures Approximating a Real-Valued Measure

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...

Markov kernels, convolution semigroups, and projective families of probability measures

For a measurable space (E,E ), we denote by E+ the set of functions E → [0,∞] that are E → B[0,∞] measurable. It can be proved that if I : E+ → [0,∞] is a function such that (i) f = 0 implies that I(f) = 0, (ii) if f, g ∈ E+ and a, b ≥ 0 then I(af + bg) = aI(f) + bI(g), and (iii) if fn is a sequence in E+ that increases pointwise to an element f of E+ then I(fn) increases to I(f), then there a ...