Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the super-replication price is the viscosity solution of a fully non-linear parabolic equation. As a by-product, we show how ε-optimal strategies can be constructed. Fina...

Abstract. The final result is presented of the NA48 experiment, performed at the CERN SPS neutral kaon beams, on the direct CP violation parameter Re(ε′/ε), as measured from the decay rates of neutral kaons into two pions. The data collected in years 1997-2001 yield the evidence for the direct CP violation with Re(ε′/ε) = (14.7± 2.2) × 10. Description of experimental method and systematics, com...

Lattice calculations of matrix elements relevant for kaon decays, and in particular for ε/ε, are reviewed. The rôle of the strange quark mass is also discussed. A comparison with other non-perturbative approaches used to compute kaon decay amplitudes is made. † Presented by G. Martinelli.

The present theoretical status of the parameter for direct CP violation ε/ε in the Standard Model is reviewed and compared with most recent experimental measurements of the same quantity. After collecting the basic expressions for ε/ε, the situation of hadronic matrix element calculations is summarised. The matrix elements constitute the dominant source of uncertainty for theoretical determinat...

Erdős and Rényi claimed and Vu proved that for all h ≥ 2 and for all ε > 0, there exists g = gh(ε) and a sequence of integers A such that the number of ordered representations of any number as a sum of h elements of A is bounded by g, and such that |A ∩ [1, x]| À x1/h−ε. We give two new proofs of this result. The first one consists of an explicit construction of such a sequence. The second one ...

In many interval computation methods, if we cannot guarantee a solution within a given interval, it often makes sense to “inflate” this interval a little bit. There exist many different “inflation” methods. The authors of PASCAL-XSC, after empirically comparing the behavior of different inflation methods, decided to implement the formula [x−, x]ε = [(1 + ε)x− − ε · x, (1 + ε)x − ε · x−]. A natu...

The eddy viscosity is the tensor in the equation that governs the transport of the large-scale (modulational) perturbations of small-scale stationary flows. As an approximation to eddy viscosity the effective tensor, that arises in the limit as the ratio between the scales ε → 0, can be considered. We are interested here in the accuracy of this approximation. We present results of computational...

In this paper, we study the theoretical properties of a class of iteratively re-weighted least squares (IRLS) algorithms for sparse signal recovery in the presence of noise. We demonstrate a one-toone correspondence between this class of algorithms and a class of Expectation-Maximization (EM) algorithms for constrained maximum likelihood estimation under a Gaussian scale mixture (GSM) distribut...