Time unit invariance is introduced as an additional requirement for multiperiod risk measures: for a constant portfolio under an i.i.d. risk factor process, the multiperiod risk should equal the one period risk of the aggregated loss, for an appropriate choice of parameters and independent of the portfolio and its distribution. Multiperiod Maximum Loss over a sequence of Kullback-Leibler balls ...

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

Given two Banach function spaces we study the pointwise product space E · F , especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E ·M(E,F ) = F , where M(E,F ) denotes the space of multiplication operators from E into F .

Let the lattice Λ have covering radius R, so that closed balls of radius R around the lattice points justcover the space. The covering multiplicity CM(Λ) is the maximal number of times the interiors of theseballs overlap. We show that the least possible covering multiplicity for an n-dimensional lattice is n ifn ≤ 8, and conjecture that it exceeds n in all other cases. We determine ...

This paper presents a novel projection-based adaptive algorithm for sparse system identification. Sequentially observed data are used to generate an equivalent number of closed convex sets, namely hyperslabs, which quantify an associated cost criterion. Sparsity is exploited by the introduction of appropriately designed weighted 1 balls. The algorithm uses only projections onto hyperslabs and w...

We adapt a construction of Klee (1981) to find a packing of unit balls in lp (1 ≤ p < ∞) which is efficient in the sense that enlarging the radius of each ball to any R > 2 covers the whole space. We show that the value 2 is optimal.

We consider the system of N (≥ 2) elastically colliding hard balls with masses m1, . . . ,mN moving uniformly in the flat unit torus T , ν ≥ 3. It is proved here that the arising billiard flow possesses the K-mixing property for almost every distribution of the masses m1, . . . ,mN .

The study of sufficient enlargements of unit balls of Banach spaces forms a natural line of attack of some well-known open problems of Banach space theory. The purpose of the paper is to present known results on sufficient enlargements and to state some open problems.

In this paper, we compare some deterministic and probabilistic techniques in the study of upper bounds in problems related to certain mean square discrepancie with respect to balls in the d-dimensional unit torus, and show that the quality of these techniques depends in an intricate way on the dimension d under consideration.